无穷维随机发展系统理论及其在碳纤维凝固浴成形机理中应用
|
摘要
本论文致力于研究无穷维随机发展系统理论及其在碳纤维凝固浴成形机理中的应用。这里的无穷维发展系统主要为泛函微分方程,偏微分方程等定义于无穷维泛函空间中的一类发展方程。同时对于被控对象,在建模过程中外部环境的噪声不可避免,或者是受到物理设备的制约使得数据测量无法准确预知,如随机噪声以及系统的状态随机切换等对系统的影响,使得随机发展方程的研究区别于普通的确定型发展方程。本文综合考虑了随机噪声,脉冲扰动、振颤扰动、时滞变化来更精确的描述被控系统,以找到更接近现实的控制策略。无穷维随机发展系统的渐近性态是近年来系统动力学研究的一个热点问题,尤其是当时间趋于无穷大时,系统的解是否收敛到某个稳态；如果收敛,以何种方式收敛的问题是无穷维随机发展系统研究中的一个基本问题。另方面,可控性作为控制理论中最基本的概念之一,无论是随机控制还是确定性控制,都越来越受到学者的重视。特别是近年来,无穷维随机发展系统在物理和工程领域得到广泛的应用。
本论文通过现代偏微分方程理论,随机分析理论和算子半群理论,致力于研究无穷维随机发展系统的稳定性和可控性,主要内容包括三部分。第一部分针对随机振颤、脉冲影响、Levy噪声和系统参数随机变化等情形,研究了一般意义下的非线性无穷维随机发展系统的稳定性和可控性问题,特别需要指出,在研究过程中,通过依分布稳定的概念,推广了我们一般意义下的均方稳定和几乎必然稳定性的结果。第二部分考虑高阶和分数阶的无穷维随机发展系统的随机指数稳定性和可控性问题。通过引入余弦算子族,正弦算子族及Caputo导数等方法与概念,得到了系统温和解稳定性和可控性的充分条件。第三部分,基于前面两部分的研究结果,结合碳纤维纺丝过程中的一些实际问题,对碳纤维凝固成形过程进行了建模,同时,通过无穷维随机发展系统的相关理论和分析方法,对于凝固成形过程的反应扩散过程的动力学方面,探讨了凝固浴条件对扩散系数及凝固能力的影响,并通过计算机仿真对碳纤维凝固浴中的反应扩散过程进行了模拟。具体而言,本文的主要研究成果体现在以下几个方面：
(1)讨论了具有脉冲影响的中立型非线性随机时滞偏微分方程温和解的稳定性。在全局Lipschitz条件、线性增长条件和压缩性条件下,利用Banach不动点定理,首次给出了具有脉冲影响的中立型非线性随机时滞发展系统的p阶矩指数稳定性和几乎必然指数稳定的充分条件,所得的结论推广了脉冲非线性无穷维随机发展系统的稳定性结果。
(2)研究了一类带脉冲响应的二阶中立型随机泛函微分系统的可控性。利用余弦算子族和正弦算子族的概念,并在相应的余弦算子族{C(t)：t∈[0,T]}与正弦算子族{S(t)：t∈[0,T]}一致有界的前提下,讨论了带脉冲响应的二阶中立型随机泛函微分方程的可控性,采用Sadovskii不动点定理,给出了系统温和解可控性的充分条件,所得的条件具有较好的保守性,并且丰富了已有的二阶发展方程的结论。
(3)讨论了带Poisson跳跃的分数阶非线性随机偏微分系统温和解的渐进稳定性。在半群理论的基础上,利用Banach不动点定理,给出了带Poisson跳跃的分数阶随机偏微分系统温和解的p阶矩渐进稳定性的充分条件,将已有的连续型模型推广到了具有随机Poisson跳跃的分段连续型模型,同时将现有的线性结果推广到了非线性的结果。
(4)研究了Hilbert空间中,由Levy过程所驱动,带Markov跳变的随机时滞反应扩散系统的依分布渐进稳定性。通过强解来近似温和解的方法,我们通过相应的强解的极限来逼近系统的温和解,并给出了由Levy鞅所驱动的带Markov跳变的随机时滞反应扩散系统的依分布渐进稳定性的充分条件,特别,所得到的结果将现有文献的相关结论推广到了参数具有Markov跳变的模型。
(5)在不确定信息下,研究了不同噪声影响下碳纤维凝固浴中扩散过程模型的渐进性质。结合算子半群与无穷维随机系统理论,研究了碳纤维凝固浴中扩散过程的模型,通过数值模拟,得到了在不确定信息下扩散机理模型的渐进性态。对于碳纤维生产过程具有实际的指导意义。
最后,总结了论文的研究内容,指出了研究中存在的不足,展望了下一步的研究方向。
In this thesis, we considered the theory of infinite dimensional stochastic evolution systems and its applications in modelling of formation mechanism in coagulation bath of carbon fiber precursor. The infinite dimensional evolution systems, defined in infinite dimensional function spaces, are described by functional differential equations, partial differential equations. The stochastic factors, considerd here, caused by modeling errors, missing measurements include random noise, impulsive effects, stochastic oscillators, time delays, system parameters random switching. As an important topic of stochastic dynamics, the stability for stochastic evolution systems in infinite dimension has gained great attention. The asymptotic behavior of stochastic evolution systems in infinite dimension, especially the convergence to a equilibrium as time goes to infinity attracts a lot of interests.
Controllability, as a fundamental concept of control theory, plays an important role both in stochastic and deterministic control theory. The study of controllability of linear and nonlinear systems represented by infinite dimensional systems in Banach spaces has been raised by many authors.
By using the theory of modern partial differential equations, stochastic analysis and the semigroup of operators, we discussed the stability and controllability of stochastic evolution systems in infinite dimension with stochastic noise, impulsive effects, stochastic perturbations, time delays and system parameters random switching.
The content of this thesis is mainly divided into three parts. Firstly, we considered the stability and controllability for infinite dimensional stochastic evolution systems with stochastic oscillators, impulsive effects, Levy noise, time delays, system parameters random switching. Especially, by the concept of stability in distribution, we generalized the results derived by mean square stability and almost surely stability, then, we discussed the exponential stability and controllability for infinite dimensional stochastic evolution systems of high order or fractional order. By using the cosine families of operators and Caputo derivate, sufficient conditions for the stability and controllability of mild solutions are obtained. In the third part, we use the theory and technique developed in previous two parts to deal with some issues of formation mechanism in coagulation bath for carbon fiber precursor. By the stochastic evolution systems theory, we modeled the formation mechanism in coagulation bath of carbon fiber precursor. The stability and controllability conditions are derived by the stochastic analysis and semigroup of operators. At last, computer simulations are given to illustrate our results.
The main contributions of the paper are as follows:
(1) The stability of mild solution for the impulsive neutral nonlinear stochastic delay partial differential equations is investigated. Under the global Lipschitz condition, linear growth condition, contractive conditions, we considered the stability in pth moment of mild solutions to nonlinear impulsive stochastic delay partial differential equations (NISDPDEs). By employing a fixed point approach, sufficient conditions for the exponential stability in pth moment of mild solutions are derived.
(2) The controllability of mild solution for a class of second order impulsive neutral stochastic functional systems is considered. We consider a class of impulsive neutral second order stochastic functional evolution equations. The Sadovskii fixed point theorem and the theory of strongly continuous cosine families of operators are used to investigate the sufficient conditions for the controllability of the system considered. An example is provided to illustrate our results. Furthermore, stability results of second order evolution equations are generalized.
(3) The asymptotic stability of mild solution to the nonlinear fractional order stochastic partial differential equations with Poisson jumps is investigated. We consider a class of fractional stochastic partial differential equations with Poisson jumps. Sufficient conditions for the existence and asymptotic stability in pth moment of mild solutions are derived by employing the semigroup of operator method, Banach fixed point principle.. The stability results of linear model are generalized to cover a class of more general nonlinear ones.
(4) In Hilbert space, we considered the asymptotic stability in distribution for stochastic delay reaction diffusion equations with Markov switching and Poisson jumps. With the help of operator in semi-group theory and stochastic systems in Hilbert space theory. Several criteria of asymptotic stability in distribution for stochastic reaction diffusion systems with delays and Markovian jumps driven by the Levy martingales in Hilbert spaces are presented. A proper approximating strong solution and a limiting type of argument are being constructed to pass on the stability of strong solutions to mild ones. Sufficient conditions are obtained to ensure the asymptotic stability in distribution for the mild solutions. In particular, stability results are generalized to cover a class of more general hybrid stochastic reaction diffusion systems with delays and jumps in infinite dimension..
(5)The asymptotic properties of the model for formation mechanism in coagulation bath of carbon fiber precursor with random informations are studied. Combining with theory of semigroup operators and stochastic analysis in Hilbert space theory, the reaction diffusion model in coagulation bath of carbon fiber precursor is considered, by numerical simulation, the asymptotic properties for the reaction diffusion model with unknown informations are investigated.
At the end, we summarize of content, advantage and the deficiency of the paper, narrate further development of the study.
本论文通过现代偏微分方程理论,随机分析理论和算子半群理论,致力于研究无穷维随机发展系统的稳定性和可控性,主要内容包括三部分。第一部分针对随机振颤、脉冲影响、Levy噪声和系统参数随机变化等情形,研究了一般意义下的非线性无穷维随机发展系统的稳定性和可控性问题,特别需要指出,在研究过程中,通过依分布稳定的概念,推广了我们一般意义下的均方稳定和几乎必然稳定性的结果。第二部分考虑高阶和分数阶的无穷维随机发展系统的随机指数稳定性和可控性问题。通过引入余弦算子族,正弦算子族及Caputo导数等方法与概念,得到了系统温和解稳定性和可控性的充分条件。第三部分,基于前面两部分的研究结果,结合碳纤维纺丝过程中的一些实际问题,对碳纤维凝固成形过程进行了建模,同时,通过无穷维随机发展系统的相关理论和分析方法,对于凝固成形过程的反应扩散过程的动力学方面,探讨了凝固浴条件对扩散系数及凝固能力的影响,并通过计算机仿真对碳纤维凝固浴中的反应扩散过程进行了模拟。具体而言,本文的主要研究成果体现在以下几个方面：
(1)讨论了具有脉冲影响的中立型非线性随机时滞偏微分方程温和解的稳定性。在全局Lipschitz条件、线性增长条件和压缩性条件下,利用Banach不动点定理,首次给出了具有脉冲影响的中立型非线性随机时滞发展系统的p阶矩指数稳定性和几乎必然指数稳定的充分条件,所得的结论推广了脉冲非线性无穷维随机发展系统的稳定性结果。
(2)研究了一类带脉冲响应的二阶中立型随机泛函微分系统的可控性。利用余弦算子族和正弦算子族的概念,并在相应的余弦算子族{C(t)：t∈[0,T]}与正弦算子族{S(t)：t∈[0,T]}一致有界的前提下,讨论了带脉冲响应的二阶中立型随机泛函微分方程的可控性,采用Sadovskii不动点定理,给出了系统温和解可控性的充分条件,所得的条件具有较好的保守性,并且丰富了已有的二阶发展方程的结论。
(3)讨论了带Poisson跳跃的分数阶非线性随机偏微分系统温和解的渐进稳定性。在半群理论的基础上,利用Banach不动点定理,给出了带Poisson跳跃的分数阶随机偏微分系统温和解的p阶矩渐进稳定性的充分条件,将已有的连续型模型推广到了具有随机Poisson跳跃的分段连续型模型,同时将现有的线性结果推广到了非线性的结果。
(4)研究了Hilbert空间中,由Levy过程所驱动,带Markov跳变的随机时滞反应扩散系统的依分布渐进稳定性。通过强解来近似温和解的方法,我们通过相应的强解的极限来逼近系统的温和解,并给出了由Levy鞅所驱动的带Markov跳变的随机时滞反应扩散系统的依分布渐进稳定性的充分条件,特别,所得到的结果将现有文献的相关结论推广到了参数具有Markov跳变的模型。
(5)在不确定信息下,研究了不同噪声影响下碳纤维凝固浴中扩散过程模型的渐进性质。结合算子半群与无穷维随机系统理论,研究了碳纤维凝固浴中扩散过程的模型,通过数值模拟,得到了在不确定信息下扩散机理模型的渐进性态。对于碳纤维生产过程具有实际的指导意义。
最后,总结了论文的研究内容,指出了研究中存在的不足,展望了下一步的研究方向。
In this thesis, we considered the theory of infinite dimensional stochastic evolution systems and its applications in modelling of formation mechanism in coagulation bath of carbon fiber precursor. The infinite dimensional evolution systems, defined in infinite dimensional function spaces, are described by functional differential equations, partial differential equations. The stochastic factors, considerd here, caused by modeling errors, missing measurements include random noise, impulsive effects, stochastic oscillators, time delays, system parameters random switching. As an important topic of stochastic dynamics, the stability for stochastic evolution systems in infinite dimension has gained great attention. The asymptotic behavior of stochastic evolution systems in infinite dimension, especially the convergence to a equilibrium as time goes to infinity attracts a lot of interests.
Controllability, as a fundamental concept of control theory, plays an important role both in stochastic and deterministic control theory. The study of controllability of linear and nonlinear systems represented by infinite dimensional systems in Banach spaces has been raised by many authors.
By using the theory of modern partial differential equations, stochastic analysis and the semigroup of operators, we discussed the stability and controllability of stochastic evolution systems in infinite dimension with stochastic noise, impulsive effects, stochastic perturbations, time delays and system parameters random switching.
The content of this thesis is mainly divided into three parts. Firstly, we considered the stability and controllability for infinite dimensional stochastic evolution systems with stochastic oscillators, impulsive effects, Levy noise, time delays, system parameters random switching. Especially, by the concept of stability in distribution, we generalized the results derived by mean square stability and almost surely stability, then, we discussed the exponential stability and controllability for infinite dimensional stochastic evolution systems of high order or fractional order. By using the cosine families of operators and Caputo derivate, sufficient conditions for the stability and controllability of mild solutions are obtained. In the third part, we use the theory and technique developed in previous two parts to deal with some issues of formation mechanism in coagulation bath for carbon fiber precursor. By the stochastic evolution systems theory, we modeled the formation mechanism in coagulation bath of carbon fiber precursor. The stability and controllability conditions are derived by the stochastic analysis and semigroup of operators. At last, computer simulations are given to illustrate our results.
The main contributions of the paper are as follows:
(1) The stability of mild solution for the impulsive neutral nonlinear stochastic delay partial differential equations is investigated. Under the global Lipschitz condition, linear growth condition, contractive conditions, we considered the stability in pth moment of mild solutions to nonlinear impulsive stochastic delay partial differential equations (NISDPDEs). By employing a fixed point approach, sufficient conditions for the exponential stability in pth moment of mild solutions are derived.
(2) The controllability of mild solution for a class of second order impulsive neutral stochastic functional systems is considered. We consider a class of impulsive neutral second order stochastic functional evolution equations. The Sadovskii fixed point theorem and the theory of strongly continuous cosine families of operators are used to investigate the sufficient conditions for the controllability of the system considered. An example is provided to illustrate our results. Furthermore, stability results of second order evolution equations are generalized.
(3) The asymptotic stability of mild solution to the nonlinear fractional order stochastic partial differential equations with Poisson jumps is investigated. We consider a class of fractional stochastic partial differential equations with Poisson jumps. Sufficient conditions for the existence and asymptotic stability in pth moment of mild solutions are derived by employing the semigroup of operator method, Banach fixed point principle.. The stability results of linear model are generalized to cover a class of more general nonlinear ones.
(4) In Hilbert space, we considered the asymptotic stability in distribution for stochastic delay reaction diffusion equations with Markov switching and Poisson jumps. With the help of operator in semi-group theory and stochastic systems in Hilbert space theory. Several criteria of asymptotic stability in distribution for stochastic reaction diffusion systems with delays and Markovian jumps driven by the Levy martingales in Hilbert spaces are presented. A proper approximating strong solution and a limiting type of argument are being constructed to pass on the stability of strong solutions to mild ones. Sufficient conditions are obtained to ensure the asymptotic stability in distribution for the mild solutions. In particular, stability results are generalized to cover a class of more general hybrid stochastic reaction diffusion systems with delays and jumps in infinite dimension..
(5)The asymptotic properties of the model for formation mechanism in coagulation bath of carbon fiber precursor with random informations are studied. Combining with theory of semigroup operators and stochastic analysis in Hilbert space theory, the reaction diffusion model in coagulation bath of carbon fiber precursor is considered, by numerical simulation, the asymptotic properties for the reaction diffusion model with unknown informations are investigated.
At the end, we summarize of content, advantage and the deficiency of the paper, narrate further development of the study.
引文
[1]L. P. Kobets, I. S. Deev, Carbon fibers:Structure and mechanical properties. Compos. Sci. Technol.,1997,57:1571-1580.
[2]张兴智,PAN基高性能碳纤维的制备及其性能的研究.安徽大学学报(自然科学版),1995,(1)：74-81.
[3]郑远.碳纤维生产技术和工业应用.兰化科技,1995,13(4)：255-260.
[4]罗益锋.新世纪初世界碳纤维透视.高科技纤维与应用,2000,25(1)：1-7.
[5]贺福,赵建国,王润娥,碳纤维工业的长足发展.高科技纤维与应用,2000,25(4)：9-13.
[6]柯泽豪,林菁菁,碳纤维研究发展之现状与未来.高科技纤维与应用,2000,25(6)：1-4.
[7]K. Sen, S. Hajir Bahrami, P. Bajaj. High-performance acrylic fibers. J. M. S.-Rev. Macromol. Chem. Phys.,1996, C36:1-7.
[8]A. K. Gupta, D. K. Paliwal, P. Bajaj. Acrylic precursors for carbon firbers. J. M.-Rev. Macromol. Chem. Phys.,1991, C31:1-89.
[9]罗益锋, 世界PAN基碳纤维发展透析及对我国的研发建议。材料导报,2000,14(11)：11-13.
[10]汪晓峰,倪如青,刘强,沃志坤,高性能聚丙烯腈基原丝的制备.合成纤维,2000,29(4)：23-27.
[11]贺福,杨永岗,突破碳纤维产业化的“瓶颈”原丝已是当务之急.碳素技术,2002,12(2)：1-4.
[12]王延相,王成国,董学梅,何东新.PAN原丝微观特征对碳纤维结构与性能的影响.金山油化纤,2002,(4)：17-22.
[13]P. Bajaj, T. V. Sreekumar, K, Sen, Structure Development during Dry-Wet Spining of Acrylonitrile/Vinyl Acids and Acrylonitrile/Methyl Acrylate Copolymers. J. Appl. Polym. Sci.,2002, (86) 773-787.
[14]贺福.高性能碳纤维原丝与干喷湿纺.高科技纤维与应用,2004,29(4).
[15]T. S. Chung, X. Hu, Effect of Air-Gap Distance on the Morphology and Thermal Properties of Polyethersulfone Hollow Fibers. J. Appl. Polym. Sci.,1997, (66) 1067-1077
[16]J. Y. Kim, H. K. Lee, K. J. Baik, S. C. Kim, liquid-liquid phase separation in polysulfone/solvent/water systems. J. Appl. Polym. Sci.,1997, (65) 2643-2653.
[17]Y. S. Soh, J. H. Kim, C. Gryte, Phase behaviour of polymer/solvent/non-solvent systems. Polymer,1995,36 (19),3711-3717.
[18]方征平.高分子物理,杭州：浙江大学出版社,2005：52-60.
[19]Minder M,膜技术基本原理(第二版),北京：清华大学出版社,1997：62-84.
[20]俞三传.浸入沉淀相转化法制膜.膜科学与技术,2000,20(5)：36-41.
[21]L. P. Cheng, D. J. Lin, C. H. Shih, PVDF membrane formation by diffusion-induced phase separation-morphology prediction based on phase behaviour and mass transfer modeling. J. Appl. Polym. Sci.,1999,37(16) 2079-2092.
[22]韩曙鹏,徐华,曹维宇,姚红,白丽芳.成纤过程中PAN纤维聚集态结构的形成.新型碳材料,2006,21(1)：11-15.
[23]S. G. Li, T. H. Boomgard, C. A. Smolders, Physical gelation of amorphous polymers in a mixture of solvent and nonsolvent. Macromolecules,1996,29, 2053-2059.
[24]S. H. Bahrami, P. Bajaj, K. Sen, Effect of coagulation condittion on properties of poly (acrylonitrile-carboxylic acid) fibers. J. Appl. Polym. Sci.,2003,89, 1825-1837.
[25]M. Monthioux, O. P. Bahl, R. B. Mathur, Controlling PAN-based carbon fiber texture via surface energetics. Carbon,2000 (38),475-494.
[26]D. R. Paul, Diffusion during the coagulation step of wet-spinning. J. Appl. Polym. Sci.,1968,12:383-402.
[27]A. Rende, A new approach to coagulation phenomena in wet-spinning. J. Appl. Polym. Sci.,1972,16:585-594.
[28]B. J. Qian, D. Pan, Z. Q. Wu, The mechanism and characteristics of dry-jet wet-spinning of acrylic fibers. Adv. Polym. Tech.,1986,6:509-529.
[29]H. Chen, R. J. Qu, Y. Liang. Kinetics of Diffusion in Polyacrylonitrile Fiber Formation. J. Appl. Polym. Sci.,2005,96:1529-1533.
[30]H. Chen, Y. Liang, C. G. Wang. Determination of the Diffusion oefficient of H2O in Polyacrylonitrile Fiber Formmion. J. Polym. Res.,2005,12:49-52
[31]汪仁钧,吴承训,潘鼎.PAN湿法纺丝凝固成形过程中的凝胶化与传质.合成技术及应用,2005,20(2)：5-8
[32]T. A. Burton, Stability by fixed point theory or Lyapunov theory:a comparison. Fixed Point Theory,2003,4,15-32.
[33]T. A. Burton, Fixed points, stability and exact linearization. Nonlinear Anal., 2005,61,857-870.
[34]T. A. Burton, Furumochi, Tetsuo, Asymptotic behavior of solutions of functional differential equations by fixed point theorems. Dynam. Systems Appl.,2002,11, 499-521.
[35]T. A. Burton, B. Zhang, Fixed points and stability of an integral equation: nonuniqueness. Appl. Math. Lett.,2004,17,839-846.
[36]M. Mariton, Jump Linear Systems in Automatic Control, New York:Marcel Dekker,1990.
[37]S. K. Ntouyas, Y. G. Sficas, P. C. Tsamatos, Existence results for initial value problems for neutral functional differential equations, J. Differ. Equations,1994, 114(2),527-537.
[38]J.K. Hale, S. M. V. Lunel, Introduction to Functional-Differential Equations, in: Applied Mathematical Sciences, vol.99, Springer-Verlag, New York,1993.
[39]T. E. Govindan, Exponential stability in mean-square of parabolic quasilinear stochastic delay evolution equations, Stoch. Anal. Appl.,1999,17,443-461.
[40]J. W. Luo, K. Liu, Stability of infinite dimensional stochastic evolution equations with memory and Markovian jumps, Stoch. Proc. Appl.,2008,5(118),864-895.
[41]T. Taniguchi, The exponential stability for stochastic delay partial differential equations, J. Math. Anal. Appl.,2007,331,191-205.
[42]Z. Hou, J. Bao, C. Yuan, Exponential stability of energy solutions to stochastic partial differential equations with variable delay and jumps. J. Math. Anal. Appl., 2010,366,44-54.
[43]K. Liu, A. Truman, A note on almost sure exponential stability for stochastic partial functional differential equations. Statist. Probab. Lett.,2000,50(3), 273-278.
[44]J. Luo, Fixed points and exponential stability of mild solutions of stochastic partial differential equations with delays. J. Math. Anal. Appl.,2008,342, 753-760.
[45]J. Luo, K. Liu, Stability of infinite dimensional stochastic evolution equations with memory and Markovian jumps. Stochastic Process. Appl.,2008,118, 864-895.
[46]M. Rockner, T. Zhang, Stochastic evolution equations of jump type:existence, uniqueness and large deviation principle. Potential Anal.,2007,26,255-279.
[47]R. Sakthivel, J. Luo, Asymptotic stability of impulsive stochastic partial differential equations with infinite delays. J.Math. Anal. Appl.,2009,356,1-6.
[48]A. Budhiraja, J. Chen, D. Paul, Large deviations for stochastic partial differential equations driven by a Poisson random measure, Stoch. Proc. Appl.,2013,2(123), 523-560.
[49]B. B. Mandelbrot, J. W. Van Ness, Fractional Brownian Motions, Fractional Noises and Applications, SIAM Review,1968,10,4.
[50]B. B. Mandelbrot, Fractals, Form and Chance and Dimension. W. H. Freeman and Co., San Franeiseo,1977.
[51]B. B. Mandelbrot, The Fractal Geometry of Nature, Freeman, NewYork,1982.
[52]Da Prato, G, Zabczyk, J. Stochastic Equations in Infinite Dimensions. Cambridge University Press,1992.
[53]Ito K. Foundations of Stochastic differential equations in infinite dimensional spaces. CBMS Notes, SIAM, Baton Rouge, Vol.47,1984.
[54]A. Ichikawa, Stability of semi-linear stochastic evolution equations, J. Math. Anal. Appl.,1982,90,12-44.
[55]E. Pardoux, Integrales stochastiques Hilbertiennes. Cahiers Mathematiques de la Decision, University Paris Dauphine, No.7617,1976.
[56]Bensoussan, A. Temam. Nonlinear Stochastic partial differential equations. Int. J. Math.,1972,11:95-121.
[57]D.A. Dawson, Stochastic evolution equations. Math Biosci.,1972,154(3-4), 187-316.
[58]N. N. Krylov, B. L. Rozovisky, Stochastic evolution equations. J. Sov. Math., 1981,38:65-113.
[59]V. V. Baklan, On the existence of solutions of stochastic equations in Hilber space. Depov Akad.nauk.Ukr.,1963,10:1299-1303.
[60]R. F. Curtain, Falb P.Stochastic differential equations in Hilbert spaces. J. Differ. Equations.,1971,10:412-430.
[61]M. A. Chojnowska, Stochastic differential equations in Hilbert spaces and some of their applications.Thesis, Institute of Methematics, Polish Academy of Sciences,1977.
[62]T. Taniguchi, K. Liu, A. Truman, Existence, uniqueness, and asymptotic behavior of mild solution to stochastic functional differential equations in Hilbert spaces. J. Differ. Equations.,2002,181:72-91.
[63]K. Liu, Lyapunov functional and asyptotic stability of stochastic delay evolution equations. Stochastics and Stochastics Reports,1998,63(1&2):1-26.
[64]J. W. Luo, Fixed points and exponential stability for stochastic Volterra-Levin equations., J. Comput. Appl. Math.,2010,234(3),934-940.
[65]K. Liu, Stability of Infinite Dimensional Stochastic Differential Equations with Applications. Chapman and Hall, CRC, London,2006.
[66]K. Liu, X. Mao, Exponential stability of non-linear stochastic evolution equations, Stochastic Process. Appl.,1998,78,173-193.
[67]V. Mandrekar, On Lyapunov stability theorems for stochastic (deterministic) evolution equations, Proc. of the NATO-ASI School on Stochastic Analysis and Applications in Physics, Nato-Asi Series (L. Streit, Ed.), Kluwer.1994,
[68]D. Ga Prato, D. Gatarek, J. Zabczyk, Invariant measures for semi-linear stochastic equations, Stoch. Anal. Appl.,1992,10,387-408.
[69]P. L. Chow, Stability of nonlinear stochastic evolution equations, J. Math. Anal. Appl.,1982,89,400-419.
[70]T. Caraballo, J. Real, On the pathwise exponential stability of nonlinear stochastic partial differential equations, Stoch. Anal. Appl.,1994,12(5),517-525.
[71]U. G. Haussmann, Asymptotic stability of the linear Ito equation in infinite dimensional. J. Math. Aanl. Appl.,1978,65:219-235.
[72]A. Ichikawa. Semelinear stochastic evolution equations:boundedness, stability and invariant measure. Stochastics.1984,12:1-39.
[73]I. Gyongy. The stability of stochastic partial differential equations and applications on supports. Lecture Notes in Mathematics, No.1390, Springer-Verlag,1989,91-118.
[74]T. Taniguchi, Asymptotic stability theorems of semilinear stochastic evolution equations in Hilbert spaces. Stochastics,1995,53,41-52.
[75]T. Caraballo, K. Liu, Exponential stability of mild solution of stochastic partial differential equations with delays. Stoch. Anal. Appl.,1999,17(5):743-763.
[76]K. Liu, A. Turman, Moment and almost sure Laypunov exponent of mild solution of stochastic evolution equations with variable delays via approximates. J. Math.Kyoto Univ.,2002,41:749-768.
[77]T. Caraballo, K. Liu, A. Truman, Stochastic functional partial differential equations:existence, uniquness and asymptotic stability. Proc. Royal Soc. London A,2000,456:1775-1802.
[78]R. Khasminskii. On the stability of solution of stochastic evolution equations. Dynki Festch.Prog.Probab,1994,34:185-197.
[79]J. W. Luo, Stability of stochastic partial differential equations with infinite delays, J. Comput. Appl. Math.,2008,222:364-371.
[80]J. W. Luo, C. H. Jin, Stability of an integro-differential equation,Comput. Math. Appl.,2009,57(7),1080-1088.
[81]Y. P. Luo, W. H. Xia, G R. Liu, F. Q. Deng, LMI approach to exponential stabilization of distributed parameter control systems with delay. Acta. Automat., 2009,35(3):299-304.
[82]罗琦.随机反应扩散方程的稳定性.华南理工大学博士学位论文.2005.
[83]M. A. Dubov, B. S. Mordukhovich, On controballability on infinite dimensional stochastic linear systems. IFAC Proceedings Series, Vol.2, Pergamon Press, New York,1987.
[84]N. I. Mahmudov, On controllability of linear stochastic systems in Hilbert spaces. J. Math. Anal. Appl.,2001,259,64-82.
[85]N. I. Mahmudov, On controllability of semilinear stochastic systems in Hilbert spaces. IMA J. Math. Control Inform,2002,19,363-376.
[86]J. P. Dauer, N. I. Mahmudov, Controllability of stochastic semilinear functional differential equations in Hilbert spaces. J. Math. Anal. Appl.,2004,290(2), 373-394.
[87]K. Balachandran, J. Dauer, Controllability of nonlinear systems in Banach spaces, J. Optim. Theory. Appl.,2002,53,345-352.
[88]R. Subalakshmi, K. Balachandran, J. Y. Park, Controllability of semilinear stochastic functional integrodifferential systems in Hilbert spaces. Nonlinear Analysis:Hybrid Sys.,2009,3(1),39-50.
[89]X. Mao, Stochastic Differential Equations and Applications. Chichester, U.K. Horwood Publishing,1997.
[90]T. E. Govindan, Almost sure exponential stability for stochastic neutral partial functional differential equations, Stochastics,2005,77,215-227.
[91]J. W. Luo, Fixed points and stability of neutral stochastic delay differential equations, J. Math. Anal. Appl.,2007,334(1),431-440.
[92]J. Randjelovic, S. Jankovic, On the pth moment exponential stability criteria of neutral stochastic functional differential equations, J. Math. Anal. Appl.,2007, 326(1),266-280.
[93]S. Jankovic, J. Randjelovic, M. Jovanovic, Razumikhin-type exponential stability criteria of neutral stochastic functional differential equations, J. Math. Anal. Appl.,2009,355(2),811-820.
[94]W. Dai, S. Hu, A new LaSalle-type theorem for stochastic differential delay equations of neutral type, Stochastic and Dynamics,2007,7(4),459-478.
[95]O.K. Jardat, A. Al-Omari, and S. Momani, Existence of the mild solution for fractional semilinear initial value problems, Nonlinear Anal.2008,69(9), 3153-3159.
[96]Z. Wei, Q. Li, J. Che, Initial value problems for fractional differential equations involving Riemann-Liouville sequential fractional derivative, J. Math. Anal. Appl.,2010,367,260-272.
[97]V. Lakshmikantham, A.S. Vatsala, Basic theory of fractional differential equations, Nonlinear Anal.,2008,69,2677-2682.
[98]C. Bai, Impulsive periodic boundary value problems for fractional differential equation involving Riemann-Liouville sequential fractional derivative, J. Math. Anal. Appl.,2011,384,211-231
[99]G. M. N Guerekata, A Cauchy problem for some fractional abstract differential equation with nonlocal conditions, Nonlinear Anal.,2009,70,1873-1876.
[100]Y. Zhou and F. Jiao, Nonlocal Cauchy problem for fractional evolution equations, Nonlinear Anal.,2010,11,4465-4475.
[101]M. M. Meerschaert, E. Nane, and P. Vellaisamy, Distributed-order fractional diffusions on bounded domains, J. Math. Anal. Appl.,2011,379,216-228.
[102]Y. Luchko, Initial-boundary-value problems for the generalized multi-term time-fractional diffusion equation, J. Math. Anal. Appl.,2011,374,538-548.
[103]V. M. Ovidiu, Universality classes for asymptotic behavior of relaxation process in systems with dynamical disorder:dynamical generalizations of stretched exponential. J. Math.Phys.,1996,37(5),2279-2306.
[104]H.Schiessel, A. Blumen, Hierarchical analogues to fractional relaxation equation, J. Phys.A:Math. Gen.,1993,26,5057-5069.
[105]F. Mainardi, Fractional relaxation-oscillation and fractional diffusion-wave phenomena. Chaos Soliton Fract.,1996,7,1461-1477.
[106]A. Y. Rossilthin, M. V. Shitikova, Analysis of rheological equations involving more than one fractional parameter by the use of the simplest mechanical systems based on these equations. Mech. Time-Depend Mat.,2001,5, 131-175.
[107]Y. E. Ryabov, A. Puzenko, Damped oscillation in view of the fractional oscillator equation. Phys. Rev. B,2002,66,184-201.
[108]B. N. N. Achar, J. W. Harmeken, T. Clarke, Damping characteristics of a fractional oscillation, PhysicaA,2004,339,311-319.
[109]R. Hilfer, Fractional diffusion based on Riemann-Liouville fractional derivatives. J. Phys. Chem. B,2000,104,3914-3917.
[110]J. R. Leith, Fractal sealing of fractional diffusion processes. Signal Process., 2003,83,2397-2409.
[111]R. Metzler, J. Klafler, Boundary value problems for fractional diffusion equations. Physica A,2000,278,107-125.
[112]W. R. Schneider, W. Wyss, Fractional diffusion and wave equations. J. Math. Phys.,1989,30(1),134-144.
[113]W. Wyss, The fractional diffusion equation. J. Math. Phys.,1986, 27(11),2782-2785.
[114]F. Mainardi, Y. Luchko, G. Pagnini, The fundamental solution of the space-time fractional diffusion equation, Fract. Calc. Appl. Anal.,2001, 4,153-192.
[115]L. R. da Silva, L. S. Lucena, E. K. Lenzi, R. S. Mendes, K. S. Fa, Fractional and nonlinear diffusion equation:additional results. Physica A,2004,344, 671-676.
[116]V. V. Anh, N. N. Leonenko, Harmonic analysis of random fractional diffusion-wave equations, Appl. Math. Comput.,2003,141,77-85.
[117]A. M. A. Eisayed, F. M. Gaafar, Fractional calculus and some intermediate Physical Processes, Appl. Math. Comput.,2003,144,117-126.
[118]W. G. Glockle, T. F. Nonnenmacher, A fractional caleulus approaeh to self-similar protein dynamics. Biophys. J.,1995,68,46-53.
[119]M. Kopf, Anomalous diffusion behavior of water in biological tissues. Biophys. J.,1996,70(6),2950-2958.
[120]G. Srinivas, A. Yethiraj, B. Bagchi, Nonexponentiality of time dependent survival reaction in polymer chain. J. Chem. Phys.,2001,114(2),9170-9179.
[121]R. R. Nigmatullin, S. I. Osokin, Signal processing and recognition of true kinetic equations containing non-integer derivatives from raw dielectric data. Signal Process.,2003,83,2433-2453.
[122]M. D. Ortigueira, On the initial conditions in continuous-time fractional linear systems. Signal Process.,2003,83,2301-2309.
[123]B. M. Vinagre, Y. Q. Chen, Fractional calculus applications in automatic control and robotics.41st IEEE Conference On Decision and Control, LasVegas, Dec.2002.
[124]J. Luo, Asymptotic behavior of solutions of second order quasilinear differential equations with delay depending on the unknown function. J. Comput. Appl. Math.,2006,185(1),133-143
[125]T.E. Govindan, N.U. Ahmed, J. Robust stabilization with a general decay of mild solutions of stochastic evolution equations. Stat. Probabil. Lett.,2013,83(1), 115-122
[126]T. Taniguchi, The existence and asymptotic behavior of mild solutions to stochastic evolution equations with infinite delays driven by Poisson jumps. Stoch. Dyn.2009,9,217-229.
[127]L. Wan, J. Duan, Exponential stability of non-autonomous stochastic partial differential equations with finite memory. Statist. Probab. Lett.,2008,78, 490-498.
[128]J. W. Luo, C. H. Jin, Stability in functional differential equations established using fixed point theory, Nonlinear Anal.-Theor.,2008,68(11),3307-3315
[129]J. W. Luo, T. Taniguchi, Fixed points and stability of stochastic neutral partial differential equations with infinite delay. Stoch. Anal. Appl.,2009,27 (6), 1163-1173.
[130]L. Jia, Z. Z. Zhang, Receiver design of UWB radio systems for an impulsive noise environment, J. Syst. Eng. Electron.,2004,1(15),31-38.
[131]R. M. Rodriguez-Osorio, L.de Haro Ariet, A. D. Castro Urbina, M. C. Ramon, A DSP-Based Impulsive Noise Generator for Test Applications, IEEE T. Ind. Electron.,2007,54(6),3397-3401.
[132]S. M. Zabin, G. A. Wright, Nonparametric density estimation and detection in impulsive interference channels. I. Estimators, IEEE T. Commun.,1994,234 (42), 1684-1697.
[133]H. H. Nguyen, T. Q. Bui, Bit-Interleaved Coded Modulation With Iterative Decoding in Impulsive Noise, IEEE T. Power Deliver,2007,1(22),151-160.
[134]X. S. Yang, J.D. Cao, J.Q. Lu, Stochastic Synchronization of Complex Networks With Nonidentical Nodes Via Hybrid Adaptive and Impulsive Control, IEEE T. Ciruits.-I,2012,2(59),371-384.
[135]J. Q. Lu, J. Kurths,; J. D. Cao, N. Mahdavi,, C. Huang, Synchronization Control for Nonlinear Stochastic Dynamical Networks:Pinning Impulsive Strategy, IEEE T. Neural Networ.,2012,2(23),285-292
[136]Y.K. Chang, Controllability of impulsive functional differential systems with infinite delay in Banach space, Chaos SolItons Fractals.,2007,33,1601-1609.
[137]R. Sakthivel, Approximate controllability of impulsive stochastic evolution equations, Funkcial Ekvac.,2009,52,381-393.
[138]Y. Ren, L. Hu, R. Sakthivel, Controllability of impulsive neutral stochastic functional differential inclusions with infinite delay, J. Math. Anal. Appl.,2011, 235,2603-2614
[139]S. K. Ntouyas and D. O. Regan, Some remarks on controllability of evolution equations in Banach spaces, Electron. J. Diff. Equ.,2009,79,1-6.
[140]J. Y. Park, S. H. Park, and Y. H. Kang, Controllability of second-order impulsive neutral functional differential inclusions in Banach spaces, Math. Method. Appl. Sci.,2009,33,249-262.
[141]R. Sakthivel, N. I. Mahmudov, and J. H. Kim, On controllability of second-order nonlinear impulsive differential systems, Nonlinear Anal.,2009,71, 45-52.
[142]M. A. Shubov, C. F. Martin, J. P. Dauer, and B. Belinskii, Exact controllability of damped wave equation, SIAM J. Control Optim.,1997,35, 1773-1789.
[143]Xiaoting Wang; Pemberton-Ross, P.; Schirmer, S.G., Symmetry and Subspace Controllability for Spin Networks with a Single-Node Control, IEEE T. Automat. Contr.,2012,8(57),1945-1956.
[144]S. G. Wang, C.Y. Wang, M.C. Zhou, Controllability Conditions of Resultant Siphons in a Class of Petri Nets. IEEE T. Syst. Man. Cy. A,2012,5(42),1206-1215.
[145]I. Kurniawan, G. Dirr, U. Helmke, Controllability Aspects of Quantum Dynamics:A Unified Approach for Closed and Open Systems. IEEE T. Automat. Contr.,2012,8(57),1984-1996.
[146]M. Egerstedt, S. Martini; M. Cao, K. Camlibel, A. Bicchi, Interacting with Networks:How Does Structure Relate to Controllability in Single-Leader, Consensus Networks? IEEE T. Cnotr. Syst. T.,2012,4(32),66-73.
[147]K. H. Yoon, Y. W. Park, Controllability of Magnetic Force in Magnetic Wheels. IEEE T. Magn.,2012,11(48),4046-4049
[148]X. L.Wang, Q. C. Zhong, Z. Q. Deng, S. Z. Yue, Current-Controlled Multiphase Slice Permanent Magnetic Bearingless Motors With Open-Circuited Phases:Fault-Tolerant Controllability and Its Verification. IEEE T. Ind. Electron., 2012,5(59),2059-2072
[149]K. Sobczyk, Stochastic Differential Equations with Applications to Physics and Engineering, Kluwei Academic Publishers, London,1991.
[150]WE. Fitzgibbon, Global existence and boundedness of solutions to the extensible beam equation, SIAM J. Math. Anal.,1982,13,739-745.
[151]X. Liu and A. R. Willims, Impulsive controllability of linear dynamical systems with applications to maneuvers of spacecraft, Math. Probl. Eng.1996 277-299.
[152]M. Benchohra, J. Henderson, and S. K. Ntouyas, Existence results for impulsive semilinear neutral functional differential equations in Banach spaces, Memoir. Differ. Equat. Math. Phys.,2002,25,105-120.
[153]E. Hernandez, M. Pierri, and G. Uniao, Existence results for an impulsive abstract partial differential equation with state-dependent delay, Comput. Math. Appl.,2006,52,411-420.
[154]Z. G. Luo, J. Xiao, Y. L. Xu, Subharmonic solutions with prescribed minimal period for some second-order impulsive differential equations, Nonlinear Anal-Theor.,2012,4(75),2249-2255
[155]H. O. Fattorini, Second-order Linear Differential Equations in Banach Spaces, in:North Holland Mathematics Studies Series, Elsevier Science, North Holland, 1985
[156]C. C. Travis, G. F.Webb, Cosine family and abstract nonlinear second-order differential equations, Acta Math. Acad. Sev. Hung. Tomus,1978,32,75-96.
[157]B. N. Sadovskii, On a fixed point principle, Funct. Anal. Appl.,1967,1, 71-74.
[158]R. L. Bagley, P. J. Torvik, On the fractional calculus model of viscoelastic behavior. J. Rheol.,1986,30(1),133-155.
[159]R. Metzler, T. F. Nonnenmacher, Fractional relaxation processes and fractional rheological models for the description of a class of viscoelastic materials. Int. J. Plasticity,2003,19,941-959.
[160]A. Chatterjee, Statistical origins of fractional derivatives in viscoelasticity. J. Sound. Vib.,2005,284,1239-1245.
[161]H. Schiessel, R. Metzler, Generalized viscoelastic models:their fractional equations with solutions. J. Phys. A:Math. Gen.,1995,28,6567-6584.
[162]S. W. J. Welch, Application of time-based fractional calculus methods to viscoelastic creep and stress relaxation of materials. Mech. Time-Depend Mat. 1999,3,279-303.
[163]M. Y. Xu, W. C. Tan, Representation of the constitutive equation of viscoelastic materials by the generalized fractional element networks and its generalized solutions, Science in China (Series G),2003,46 (2),145-157.
[164]S. Kempfle, Fractional calculus via functional calculus:theory and applications. Nonlinear Dynam.,2002,29,99-127.
[165]Y. Ding, Z. Wang, H. Ye, Optimal control of a fractional order HIV-immune system with memory, IEEE T. Contr. Syst. T.2012,20 (3),763-769.
[166]Y. Jiang, X. Wang, Y. Wang, On a stochastic heat equation with first order fractional noises and applications to finance, J. Math. Anal. Appl. in press.
[167]E. Kaslika, S. Sivasundaram, Nonlinear dynamics and chaos in fractional-order neural networks, Neural Networks,2012,32,245-256.
[168]J. He, Approximate analytical solution for seepage flow with fractional derivatives in porous media, Comput. Methods Appl. Mech. Engg.,1998,167, 57-68.
[169]D. Delbosco, L. Rodino, Existence and uniqueness for a nonlinear fractional differential equation, J. Math. Anal. Appl.,1996,204,609-625.
[170]D. Wu, On the solution process for a stochastic fractional partial differential equation driven by space-time white noise, Statist. Probab. Lett.,2011,81, 1161-1172.
[171]Y. T. Su, K.T.Wong, K. P. Ho, Linear MMSE Estimation of Large Magnitude Symmetric Levy-Process Phase-Noise, IEEE T. Commun.,2010, 12(58),3369-3374.
[172]D. Song, Optimal integrated ordering and production policy in a supply chain with stochastic lead-time, processing-time, and demand, IEEE Trans. Autom. Control,2009,54 (9),2027-2041.
[173]D. Seo, H. Lee, Stationary waiting times in m-node tandem queues with production blocking, IEEE Trans. Automat. Control,2011,56 (4),958-961,
[174]M. Taheri, K. Navaie, M. Bastani, On the outage probability of SIR-based power-controlled DS-CDMA networks with spatial Poisson traffic, IEEE Trans. Veh. Technol.,2010,59 (1),499-506.
[175]Z. J. Jurek, Invariant measures under random integral mappings and marginal distributions of fractional Levy processes, Stat. Probabil. Lett.,2013,1(83), 177-183.
[176]M. Rockner, T. Zhang, Stochastic evolution equations of jump type: existence, uniqueness and large deviation principle. Potential Anal.2007,26, 255-279.
[177]Z. Hou, J. Bao, C. Yuan, Exponential stability of energy solutions to stochastic partial differential equations with variable delay and jumps. J. Math. Anal. Appl.,2010,366,44-54.
[178]J. Cui, L. Yan, X. Sun, Exponential stability for neutral stochastic partial differential equations with delays and Poisson jumps, Statist. Probab. Lett.,2011, 81,1970-1977.
[179]K. Shi, Y. Wang, On a stochastic fractional partial differential equation driven by a Levy space-time white noise, J. Math. Anal. Appl.,2010,364, 119-129.
[180]A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, in:North-Holland Mathematics Studies, vol. 204, Elsevier Science B.V., Amsterdam,2006.
[181]M.M. El-Borai, Some probability densities and fundamental solutions of fractional evolution equations, Chaos, SolItons and Fract.,2002,14,433-440.
[182]J. Wang, Y. Zhou, A class of fractional evolution equations and optimal controls, Nonlinear Anal.2011,12,262-272.
[183]F.Mainardi, P. Paradisi, and R. Gorenflo, Probability distributions generated by fractional diffusion equations, in:J. Kertesz, I. Kondor (Eds.), Econophysics: An Emerging Science, Kluwer, Dordrecht,2000.
[184]D. Applebaum, Levy Processes and Stochastic Calculus, Cambridge University Press,2004.
[185]D. Song, Optimal integrated ordering and production policy in a supply chain with stochastic lead-time, processing-time, and demand, IEEE Trans. Autom. Control,2009,54 (9),2027-2041.
[186]X. Mao, A. Matasov, and A. Piunovskiy, Stochastic differential delay equations with Markovian switching, Bernoulli,20006 (1),73-90.
[187]J. Wang, H. Wu, and H. Li, Stochastically exponential stability and stabilization of uncertain linear hyperbolic PDE systems with Markov jumping parameters, Automatica,2012,48,569-576.
[188]J. Feng, J. Lam, and Z. Shu, Stabilization of Markovian systems via probability rate synthesis and output feedback, IEEE Trans. Automat. Control, 2010,55(3),773-777.
[189]M. Tanelli, B. Picasso, P. Bolzern, and P. Colaneri, Almost sure stabilization of uncertain continuous-Time Markov jump linear systems, IEEE Trans. Automat. Control,2010,55(1),195-201.
[190]X. Mao, Stability of stochastic differential equations with Markovian switching, Stochastic Process Appl.,1999,79,45-67.
[191]X. Mao, Exponential stability of stochastic delay interval systems with Markovian switching, IEEE Trans. Automat. Control,2002,47(10),1604-1612.
[192]S. Adlakha, S. Lall and A. Goldsmith, Networked Markov decision processes with delays, IEEE Trans. Automat. Control,2012,57(4),1013-1018.
[193]W. Li and Y. Jia, Consensus-based distributed multiple model UKF for jump Markov nonlinear systems, IEEE Trans. Automat. Control,2012,57(1),230-236,.
[194]J. W. Dong, Classical solutions to the one-dimensional stationary quantum drift-diffusion model, J. Math. Anal. Appl.,2013,399(2),594-598.
[195]D. Applebaum, Martingale-valued measures, Ornstein-Uhlenbeck processes with jumps and operator self-decomposability in Hilbert space, in:M. Emery, M. Yor (Eds.), Seminaire de Probabilities,2006,39, in:LNM, vol.1874, Springer, 171-197.
[196]D. Seo and H. Lee, Stationary waiting times in m-Node tandem queues with Production blocking, IEEE Trans. Automat. Control,2011,56(4),958-961.
[197]M. Taheri, K. Navaie, and M. Bastani, On the outage probability of SIR-based power-controlled DS-CDMA networks with spatial Poisson traffic, IEEE Trans. Veh. Technol.,2010,59(1),499-506.
[198]S. Peng and Y. Zhang, Some new criteria on pth moment stability of stochastic functional differential equations with markovian switching, IEEE Trans. Autom. Control,2010,55(12),2886-2890.
[199]S. Aihara, On adaptive boundary control for stochastic parabolic systems with unknown potential coefficient, IEEE Trans. Autom. Control,1997,42 (3), 350-363.
[200]J. Wang, B. Ren, and M. Krstic, Stabilization and gevrey regularity of a Schrodinger equation in boundary feedback with a heat equation, IEEE Trans. Autom. Control,2012,57 (1),179-185.
[201]A. K. Drame, D. Dochain, and J. J. Winkin, Asymptotic behavior and stability for solutions of a biochemical reactor distributed parameter Model, IEEE Trans. Autom. Control,2008,53(1),412-416.
[2]张兴智,PAN基高性能碳纤维的制备及其性能的研究.安徽大学学报(自然科学版),1995,(1)：74-81.
[3]郑远.碳纤维生产技术和工业应用.兰化科技,1995,13(4)：255-260.
[4]罗益锋.新世纪初世界碳纤维透视.高科技纤维与应用,2000,25(1)：1-7.
[5]贺福,赵建国,王润娥,碳纤维工业的长足发展.高科技纤维与应用,2000,25(4)：9-13.
[6]柯泽豪,林菁菁,碳纤维研究发展之现状与未来.高科技纤维与应用,2000,25(6)：1-4.
[7]K. Sen, S. Hajir Bahrami, P. Bajaj. High-performance acrylic fibers. J. M. S.-Rev. Macromol. Chem. Phys.,1996, C36:1-7.
[8]A. K. Gupta, D. K. Paliwal, P. Bajaj. Acrylic precursors for carbon firbers. J. M.-Rev. Macromol. Chem. Phys.,1991, C31:1-89.
[9]罗益锋, 世界PAN基碳纤维发展透析及对我国的研发建议。材料导报,2000,14(11)：11-13.
[10]汪晓峰,倪如青,刘强,沃志坤,高性能聚丙烯腈基原丝的制备.合成纤维,2000,29(4)：23-27.
[11]贺福,杨永岗,突破碳纤维产业化的“瓶颈”原丝已是当务之急.碳素技术,2002,12(2)：1-4.
[12]王延相,王成国,董学梅,何东新.PAN原丝微观特征对碳纤维结构与性能的影响.金山油化纤,2002,(4)：17-22.
[13]P. Bajaj, T. V. Sreekumar, K, Sen, Structure Development during Dry-Wet Spining of Acrylonitrile/Vinyl Acids and Acrylonitrile/Methyl Acrylate Copolymers. J. Appl. Polym. Sci.,2002, (86) 773-787.
[14]贺福.高性能碳纤维原丝与干喷湿纺.高科技纤维与应用,2004,29(4).
[15]T. S. Chung, X. Hu, Effect of Air-Gap Distance on the Morphology and Thermal Properties of Polyethersulfone Hollow Fibers. J. Appl. Polym. Sci.,1997, (66) 1067-1077
[16]J. Y. Kim, H. K. Lee, K. J. Baik, S. C. Kim, liquid-liquid phase separation in polysulfone/solvent/water systems. J. Appl. Polym. Sci.,1997, (65) 2643-2653.
[17]Y. S. Soh, J. H. Kim, C. Gryte, Phase behaviour of polymer/solvent/non-solvent systems. Polymer,1995,36 (19),3711-3717.
[18]方征平.高分子物理,杭州：浙江大学出版社,2005：52-60.
[19]Minder M,膜技术基本原理(第二版),北京：清华大学出版社,1997：62-84.
[20]俞三传.浸入沉淀相转化法制膜.膜科学与技术,2000,20(5)：36-41.
[21]L. P. Cheng, D. J. Lin, C. H. Shih, PVDF membrane formation by diffusion-induced phase separation-morphology prediction based on phase behaviour and mass transfer modeling. J. Appl. Polym. Sci.,1999,37(16) 2079-2092.
[22]韩曙鹏,徐华,曹维宇,姚红,白丽芳.成纤过程中PAN纤维聚集态结构的形成.新型碳材料,2006,21(1)：11-15.
[23]S. G. Li, T. H. Boomgard, C. A. Smolders, Physical gelation of amorphous polymers in a mixture of solvent and nonsolvent. Macromolecules,1996,29, 2053-2059.
[24]S. H. Bahrami, P. Bajaj, K. Sen, Effect of coagulation condittion on properties of poly (acrylonitrile-carboxylic acid) fibers. J. Appl. Polym. Sci.,2003,89, 1825-1837.
[25]M. Monthioux, O. P. Bahl, R. B. Mathur, Controlling PAN-based carbon fiber texture via surface energetics. Carbon,2000 (38),475-494.
[26]D. R. Paul, Diffusion during the coagulation step of wet-spinning. J. Appl. Polym. Sci.,1968,12:383-402.
[27]A. Rende, A new approach to coagulation phenomena in wet-spinning. J. Appl. Polym. Sci.,1972,16:585-594.
[28]B. J. Qian, D. Pan, Z. Q. Wu, The mechanism and characteristics of dry-jet wet-spinning of acrylic fibers. Adv. Polym. Tech.,1986,6:509-529.
[29]H. Chen, R. J. Qu, Y. Liang. Kinetics of Diffusion in Polyacrylonitrile Fiber Formation. J. Appl. Polym. Sci.,2005,96:1529-1533.
[30]H. Chen, Y. Liang, C. G. Wang. Determination of the Diffusion oefficient of H2O in Polyacrylonitrile Fiber Formmion. J. Polym. Res.,2005,12:49-52
[31]汪仁钧,吴承训,潘鼎.PAN湿法纺丝凝固成形过程中的凝胶化与传质.合成技术及应用,2005,20(2)：5-8
[32]T. A. Burton, Stability by fixed point theory or Lyapunov theory:a comparison. Fixed Point Theory,2003,4,15-32.
[33]T. A. Burton, Fixed points, stability and exact linearization. Nonlinear Anal., 2005,61,857-870.
[34]T. A. Burton, Furumochi, Tetsuo, Asymptotic behavior of solutions of functional differential equations by fixed point theorems. Dynam. Systems Appl.,2002,11, 499-521.
[35]T. A. Burton, B. Zhang, Fixed points and stability of an integral equation: nonuniqueness. Appl. Math. Lett.,2004,17,839-846.
[36]M. Mariton, Jump Linear Systems in Automatic Control, New York:Marcel Dekker,1990.
[37]S. K. Ntouyas, Y. G. Sficas, P. C. Tsamatos, Existence results for initial value problems for neutral functional differential equations, J. Differ. Equations,1994, 114(2),527-537.
[38]J.K. Hale, S. M. V. Lunel, Introduction to Functional-Differential Equations, in: Applied Mathematical Sciences, vol.99, Springer-Verlag, New York,1993.
[39]T. E. Govindan, Exponential stability in mean-square of parabolic quasilinear stochastic delay evolution equations, Stoch. Anal. Appl.,1999,17,443-461.
[40]J. W. Luo, K. Liu, Stability of infinite dimensional stochastic evolution equations with memory and Markovian jumps, Stoch. Proc. Appl.,2008,5(118),864-895.
[41]T. Taniguchi, The exponential stability for stochastic delay partial differential equations, J. Math. Anal. Appl.,2007,331,191-205.
[42]Z. Hou, J. Bao, C. Yuan, Exponential stability of energy solutions to stochastic partial differential equations with variable delay and jumps. J. Math. Anal. Appl., 2010,366,44-54.
[43]K. Liu, A. Truman, A note on almost sure exponential stability for stochastic partial functional differential equations. Statist. Probab. Lett.,2000,50(3), 273-278.
[44]J. Luo, Fixed points and exponential stability of mild solutions of stochastic partial differential equations with delays. J. Math. Anal. Appl.,2008,342, 753-760.
[45]J. Luo, K. Liu, Stability of infinite dimensional stochastic evolution equations with memory and Markovian jumps. Stochastic Process. Appl.,2008,118, 864-895.
[46]M. Rockner, T. Zhang, Stochastic evolution equations of jump type:existence, uniqueness and large deviation principle. Potential Anal.,2007,26,255-279.
[47]R. Sakthivel, J. Luo, Asymptotic stability of impulsive stochastic partial differential equations with infinite delays. J.Math. Anal. Appl.,2009,356,1-6.
[48]A. Budhiraja, J. Chen, D. Paul, Large deviations for stochastic partial differential equations driven by a Poisson random measure, Stoch. Proc. Appl.,2013,2(123), 523-560.
[49]B. B. Mandelbrot, J. W. Van Ness, Fractional Brownian Motions, Fractional Noises and Applications, SIAM Review,1968,10,4.
[50]B. B. Mandelbrot, Fractals, Form and Chance and Dimension. W. H. Freeman and Co., San Franeiseo,1977.
[51]B. B. Mandelbrot, The Fractal Geometry of Nature, Freeman, NewYork,1982.
[52]Da Prato, G, Zabczyk, J. Stochastic Equations in Infinite Dimensions. Cambridge University Press,1992.
[53]Ito K. Foundations of Stochastic differential equations in infinite dimensional spaces. CBMS Notes, SIAM, Baton Rouge, Vol.47,1984.
[54]A. Ichikawa, Stability of semi-linear stochastic evolution equations, J. Math. Anal. Appl.,1982,90,12-44.
[55]E. Pardoux, Integrales stochastiques Hilbertiennes. Cahiers Mathematiques de la Decision, University Paris Dauphine, No.7617,1976.
[56]Bensoussan, A. Temam. Nonlinear Stochastic partial differential equations. Int. J. Math.,1972,11:95-121.
[57]D.A. Dawson, Stochastic evolution equations. Math Biosci.,1972,154(3-4), 187-316.
[58]N. N. Krylov, B. L. Rozovisky, Stochastic evolution equations. J. Sov. Math., 1981,38:65-113.
[59]V. V. Baklan, On the existence of solutions of stochastic equations in Hilber space. Depov Akad.nauk.Ukr.,1963,10:1299-1303.
[60]R. F. Curtain, Falb P.Stochastic differential equations in Hilbert spaces. J. Differ. Equations.,1971,10:412-430.
[61]M. A. Chojnowska, Stochastic differential equations in Hilbert spaces and some of their applications.Thesis, Institute of Methematics, Polish Academy of Sciences,1977.
[62]T. Taniguchi, K. Liu, A. Truman, Existence, uniqueness, and asymptotic behavior of mild solution to stochastic functional differential equations in Hilbert spaces. J. Differ. Equations.,2002,181:72-91.
[63]K. Liu, Lyapunov functional and asyptotic stability of stochastic delay evolution equations. Stochastics and Stochastics Reports,1998,63(1&2):1-26.
[64]J. W. Luo, Fixed points and exponential stability for stochastic Volterra-Levin equations., J. Comput. Appl. Math.,2010,234(3),934-940.
[65]K. Liu, Stability of Infinite Dimensional Stochastic Differential Equations with Applications. Chapman and Hall, CRC, London,2006.
[66]K. Liu, X. Mao, Exponential stability of non-linear stochastic evolution equations, Stochastic Process. Appl.,1998,78,173-193.
[67]V. Mandrekar, On Lyapunov stability theorems for stochastic (deterministic) evolution equations, Proc. of the NATO-ASI School on Stochastic Analysis and Applications in Physics, Nato-Asi Series (L. Streit, Ed.), Kluwer.1994,
[68]D. Ga Prato, D. Gatarek, J. Zabczyk, Invariant measures for semi-linear stochastic equations, Stoch. Anal. Appl.,1992,10,387-408.
[69]P. L. Chow, Stability of nonlinear stochastic evolution equations, J. Math. Anal. Appl.,1982,89,400-419.
[70]T. Caraballo, J. Real, On the pathwise exponential stability of nonlinear stochastic partial differential equations, Stoch. Anal. Appl.,1994,12(5),517-525.
[71]U. G. Haussmann, Asymptotic stability of the linear Ito equation in infinite dimensional. J. Math. Aanl. Appl.,1978,65:219-235.
[72]A. Ichikawa. Semelinear stochastic evolution equations:boundedness, stability and invariant measure. Stochastics.1984,12:1-39.
[73]I. Gyongy. The stability of stochastic partial differential equations and applications on supports. Lecture Notes in Mathematics, No.1390, Springer-Verlag,1989,91-118.
[74]T. Taniguchi, Asymptotic stability theorems of semilinear stochastic evolution equations in Hilbert spaces. Stochastics,1995,53,41-52.
[75]T. Caraballo, K. Liu, Exponential stability of mild solution of stochastic partial differential equations with delays. Stoch. Anal. Appl.,1999,17(5):743-763.
[76]K. Liu, A. Turman, Moment and almost sure Laypunov exponent of mild solution of stochastic evolution equations with variable delays via approximates. J. Math.Kyoto Univ.,2002,41:749-768.
[77]T. Caraballo, K. Liu, A. Truman, Stochastic functional partial differential equations:existence, uniquness and asymptotic stability. Proc. Royal Soc. London A,2000,456:1775-1802.
[78]R. Khasminskii. On the stability of solution of stochastic evolution equations. Dynki Festch.Prog.Probab,1994,34:185-197.
[79]J. W. Luo, Stability of stochastic partial differential equations with infinite delays, J. Comput. Appl. Math.,2008,222:364-371.
[80]J. W. Luo, C. H. Jin, Stability of an integro-differential equation,Comput. Math. Appl.,2009,57(7),1080-1088.
[81]Y. P. Luo, W. H. Xia, G R. Liu, F. Q. Deng, LMI approach to exponential stabilization of distributed parameter control systems with delay. Acta. Automat., 2009,35(3):299-304.
[82]罗琦.随机反应扩散方程的稳定性.华南理工大学博士学位论文.2005.
[83]M. A. Dubov, B. S. Mordukhovich, On controballability on infinite dimensional stochastic linear systems. IFAC Proceedings Series, Vol.2, Pergamon Press, New York,1987.
[84]N. I. Mahmudov, On controllability of linear stochastic systems in Hilbert spaces. J. Math. Anal. Appl.,2001,259,64-82.
[85]N. I. Mahmudov, On controllability of semilinear stochastic systems in Hilbert spaces. IMA J. Math. Control Inform,2002,19,363-376.
[86]J. P. Dauer, N. I. Mahmudov, Controllability of stochastic semilinear functional differential equations in Hilbert spaces. J. Math. Anal. Appl.,2004,290(2), 373-394.
[87]K. Balachandran, J. Dauer, Controllability of nonlinear systems in Banach spaces, J. Optim. Theory. Appl.,2002,53,345-352.
[88]R. Subalakshmi, K. Balachandran, J. Y. Park, Controllability of semilinear stochastic functional integrodifferential systems in Hilbert spaces. Nonlinear Analysis:Hybrid Sys.,2009,3(1),39-50.
[89]X. Mao, Stochastic Differential Equations and Applications. Chichester, U.K. Horwood Publishing,1997.
[90]T. E. Govindan, Almost sure exponential stability for stochastic neutral partial functional differential equations, Stochastics,2005,77,215-227.
[91]J. W. Luo, Fixed points and stability of neutral stochastic delay differential equations, J. Math. Anal. Appl.,2007,334(1),431-440.
[92]J. Randjelovic, S. Jankovic, On the pth moment exponential stability criteria of neutral stochastic functional differential equations, J. Math. Anal. Appl.,2007, 326(1),266-280.
[93]S. Jankovic, J. Randjelovic, M. Jovanovic, Razumikhin-type exponential stability criteria of neutral stochastic functional differential equations, J. Math. Anal. Appl.,2009,355(2),811-820.
[94]W. Dai, S. Hu, A new LaSalle-type theorem for stochastic differential delay equations of neutral type, Stochastic and Dynamics,2007,7(4),459-478.
[95]O.K. Jardat, A. Al-Omari, and S. Momani, Existence of the mild solution for fractional semilinear initial value problems, Nonlinear Anal.2008,69(9), 3153-3159.
[96]Z. Wei, Q. Li, J. Che, Initial value problems for fractional differential equations involving Riemann-Liouville sequential fractional derivative, J. Math. Anal. Appl.,2010,367,260-272.
[97]V. Lakshmikantham, A.S. Vatsala, Basic theory of fractional differential equations, Nonlinear Anal.,2008,69,2677-2682.
[98]C. Bai, Impulsive periodic boundary value problems for fractional differential equation involving Riemann-Liouville sequential fractional derivative, J. Math. Anal. Appl.,2011,384,211-231
[99]G. M. N Guerekata, A Cauchy problem for some fractional abstract differential equation with nonlocal conditions, Nonlinear Anal.,2009,70,1873-1876.
[100]Y. Zhou and F. Jiao, Nonlocal Cauchy problem for fractional evolution equations, Nonlinear Anal.,2010,11,4465-4475.
[101]M. M. Meerschaert, E. Nane, and P. Vellaisamy, Distributed-order fractional diffusions on bounded domains, J. Math. Anal. Appl.,2011,379,216-228.
[102]Y. Luchko, Initial-boundary-value problems for the generalized multi-term time-fractional diffusion equation, J. Math. Anal. Appl.,2011,374,538-548.
[103]V. M. Ovidiu, Universality classes for asymptotic behavior of relaxation process in systems with dynamical disorder:dynamical generalizations of stretched exponential. J. Math.Phys.,1996,37(5),2279-2306.
[104]H.Schiessel, A. Blumen, Hierarchical analogues to fractional relaxation equation, J. Phys.A:Math. Gen.,1993,26,5057-5069.
[105]F. Mainardi, Fractional relaxation-oscillation and fractional diffusion-wave phenomena. Chaos Soliton Fract.,1996,7,1461-1477.
[106]A. Y. Rossilthin, M. V. Shitikova, Analysis of rheological equations involving more than one fractional parameter by the use of the simplest mechanical systems based on these equations. Mech. Time-Depend Mat.,2001,5, 131-175.
[107]Y. E. Ryabov, A. Puzenko, Damped oscillation in view of the fractional oscillator equation. Phys. Rev. B,2002,66,184-201.
[108]B. N. N. Achar, J. W. Harmeken, T. Clarke, Damping characteristics of a fractional oscillation, PhysicaA,2004,339,311-319.
[109]R. Hilfer, Fractional diffusion based on Riemann-Liouville fractional derivatives. J. Phys. Chem. B,2000,104,3914-3917.
[110]J. R. Leith, Fractal sealing of fractional diffusion processes. Signal Process., 2003,83,2397-2409.
[111]R. Metzler, J. Klafler, Boundary value problems for fractional diffusion equations. Physica A,2000,278,107-125.
[112]W. R. Schneider, W. Wyss, Fractional diffusion and wave equations. J. Math. Phys.,1989,30(1),134-144.
[113]W. Wyss, The fractional diffusion equation. J. Math. Phys.,1986, 27(11),2782-2785.
[114]F. Mainardi, Y. Luchko, G. Pagnini, The fundamental solution of the space-time fractional diffusion equation, Fract. Calc. Appl. Anal.,2001, 4,153-192.
[115]L. R. da Silva, L. S. Lucena, E. K. Lenzi, R. S. Mendes, K. S. Fa, Fractional and nonlinear diffusion equation:additional results. Physica A,2004,344, 671-676.
[116]V. V. Anh, N. N. Leonenko, Harmonic analysis of random fractional diffusion-wave equations, Appl. Math. Comput.,2003,141,77-85.
[117]A. M. A. Eisayed, F. M. Gaafar, Fractional calculus and some intermediate Physical Processes, Appl. Math. Comput.,2003,144,117-126.
[118]W. G. Glockle, T. F. Nonnenmacher, A fractional caleulus approaeh to self-similar protein dynamics. Biophys. J.,1995,68,46-53.
[119]M. Kopf, Anomalous diffusion behavior of water in biological tissues. Biophys. J.,1996,70(6),2950-2958.
[120]G. Srinivas, A. Yethiraj, B. Bagchi, Nonexponentiality of time dependent survival reaction in polymer chain. J. Chem. Phys.,2001,114(2),9170-9179.
[121]R. R. Nigmatullin, S. I. Osokin, Signal processing and recognition of true kinetic equations containing non-integer derivatives from raw dielectric data. Signal Process.,2003,83,2433-2453.
[122]M. D. Ortigueira, On the initial conditions in continuous-time fractional linear systems. Signal Process.,2003,83,2301-2309.
[123]B. M. Vinagre, Y. Q. Chen, Fractional calculus applications in automatic control and robotics.41st IEEE Conference On Decision and Control, LasVegas, Dec.2002.
[124]J. Luo, Asymptotic behavior of solutions of second order quasilinear differential equations with delay depending on the unknown function. J. Comput. Appl. Math.,2006,185(1),133-143
[125]T.E. Govindan, N.U. Ahmed, J. Robust stabilization with a general decay of mild solutions of stochastic evolution equations. Stat. Probabil. Lett.,2013,83(1), 115-122
[126]T. Taniguchi, The existence and asymptotic behavior of mild solutions to stochastic evolution equations with infinite delays driven by Poisson jumps. Stoch. Dyn.2009,9,217-229.
[127]L. Wan, J. Duan, Exponential stability of non-autonomous stochastic partial differential equations with finite memory. Statist. Probab. Lett.,2008,78, 490-498.
[128]J. W. Luo, C. H. Jin, Stability in functional differential equations established using fixed point theory, Nonlinear Anal.-Theor.,2008,68(11),3307-3315
[129]J. W. Luo, T. Taniguchi, Fixed points and stability of stochastic neutral partial differential equations with infinite delay. Stoch. Anal. Appl.,2009,27 (6), 1163-1173.
[130]L. Jia, Z. Z. Zhang, Receiver design of UWB radio systems for an impulsive noise environment, J. Syst. Eng. Electron.,2004,1(15),31-38.
[131]R. M. Rodriguez-Osorio, L.de Haro Ariet, A. D. Castro Urbina, M. C. Ramon, A DSP-Based Impulsive Noise Generator for Test Applications, IEEE T. Ind. Electron.,2007,54(6),3397-3401.
[132]S. M. Zabin, G. A. Wright, Nonparametric density estimation and detection in impulsive interference channels. I. Estimators, IEEE T. Commun.,1994,234 (42), 1684-1697.
[133]H. H. Nguyen, T. Q. Bui, Bit-Interleaved Coded Modulation With Iterative Decoding in Impulsive Noise, IEEE T. Power Deliver,2007,1(22),151-160.
[134]X. S. Yang, J.D. Cao, J.Q. Lu, Stochastic Synchronization of Complex Networks With Nonidentical Nodes Via Hybrid Adaptive and Impulsive Control, IEEE T. Ciruits.-I,2012,2(59),371-384.
[135]J. Q. Lu, J. Kurths,; J. D. Cao, N. Mahdavi,, C. Huang, Synchronization Control for Nonlinear Stochastic Dynamical Networks:Pinning Impulsive Strategy, IEEE T. Neural Networ.,2012,2(23),285-292
[136]Y.K. Chang, Controllability of impulsive functional differential systems with infinite delay in Banach space, Chaos SolItons Fractals.,2007,33,1601-1609.
[137]R. Sakthivel, Approximate controllability of impulsive stochastic evolution equations, Funkcial Ekvac.,2009,52,381-393.
[138]Y. Ren, L. Hu, R. Sakthivel, Controllability of impulsive neutral stochastic functional differential inclusions with infinite delay, J. Math. Anal. Appl.,2011, 235,2603-2614
[139]S. K. Ntouyas and D. O. Regan, Some remarks on controllability of evolution equations in Banach spaces, Electron. J. Diff. Equ.,2009,79,1-6.
[140]J. Y. Park, S. H. Park, and Y. H. Kang, Controllability of second-order impulsive neutral functional differential inclusions in Banach spaces, Math. Method. Appl. Sci.,2009,33,249-262.
[141]R. Sakthivel, N. I. Mahmudov, and J. H. Kim, On controllability of second-order nonlinear impulsive differential systems, Nonlinear Anal.,2009,71, 45-52.
[142]M. A. Shubov, C. F. Martin, J. P. Dauer, and B. Belinskii, Exact controllability of damped wave equation, SIAM J. Control Optim.,1997,35, 1773-1789.
[143]Xiaoting Wang; Pemberton-Ross, P.; Schirmer, S.G., Symmetry and Subspace Controllability for Spin Networks with a Single-Node Control, IEEE T. Automat. Contr.,2012,8(57),1945-1956.
[144]S. G. Wang, C.Y. Wang, M.C. Zhou, Controllability Conditions of Resultant Siphons in a Class of Petri Nets. IEEE T. Syst. Man. Cy. A,2012,5(42),1206-1215.
[145]I. Kurniawan, G. Dirr, U. Helmke, Controllability Aspects of Quantum Dynamics:A Unified Approach for Closed and Open Systems. IEEE T. Automat. Contr.,2012,8(57),1984-1996.
[146]M. Egerstedt, S. Martini; M. Cao, K. Camlibel, A. Bicchi, Interacting with Networks:How Does Structure Relate to Controllability in Single-Leader, Consensus Networks? IEEE T. Cnotr. Syst. T.,2012,4(32),66-73.
[147]K. H. Yoon, Y. W. Park, Controllability of Magnetic Force in Magnetic Wheels. IEEE T. Magn.,2012,11(48),4046-4049
[148]X. L.Wang, Q. C. Zhong, Z. Q. Deng, S. Z. Yue, Current-Controlled Multiphase Slice Permanent Magnetic Bearingless Motors With Open-Circuited Phases:Fault-Tolerant Controllability and Its Verification. IEEE T. Ind. Electron., 2012,5(59),2059-2072
[149]K. Sobczyk, Stochastic Differential Equations with Applications to Physics and Engineering, Kluwei Academic Publishers, London,1991.
[150]WE. Fitzgibbon, Global existence and boundedness of solutions to the extensible beam equation, SIAM J. Math. Anal.,1982,13,739-745.
[151]X. Liu and A. R. Willims, Impulsive controllability of linear dynamical systems with applications to maneuvers of spacecraft, Math. Probl. Eng.1996 277-299.
[152]M. Benchohra, J. Henderson, and S. K. Ntouyas, Existence results for impulsive semilinear neutral functional differential equations in Banach spaces, Memoir. Differ. Equat. Math. Phys.,2002,25,105-120.
[153]E. Hernandez, M. Pierri, and G. Uniao, Existence results for an impulsive abstract partial differential equation with state-dependent delay, Comput. Math. Appl.,2006,52,411-420.
[154]Z. G. Luo, J. Xiao, Y. L. Xu, Subharmonic solutions with prescribed minimal period for some second-order impulsive differential equations, Nonlinear Anal-Theor.,2012,4(75),2249-2255
[155]H. O. Fattorini, Second-order Linear Differential Equations in Banach Spaces, in:North Holland Mathematics Studies Series, Elsevier Science, North Holland, 1985
[156]C. C. Travis, G. F.Webb, Cosine family and abstract nonlinear second-order differential equations, Acta Math. Acad. Sev. Hung. Tomus,1978,32,75-96.
[157]B. N. Sadovskii, On a fixed point principle, Funct. Anal. Appl.,1967,1, 71-74.
[158]R. L. Bagley, P. J. Torvik, On the fractional calculus model of viscoelastic behavior. J. Rheol.,1986,30(1),133-155.
[159]R. Metzler, T. F. Nonnenmacher, Fractional relaxation processes and fractional rheological models for the description of a class of viscoelastic materials. Int. J. Plasticity,2003,19,941-959.
[160]A. Chatterjee, Statistical origins of fractional derivatives in viscoelasticity. J. Sound. Vib.,2005,284,1239-1245.
[161]H. Schiessel, R. Metzler, Generalized viscoelastic models:their fractional equations with solutions. J. Phys. A:Math. Gen.,1995,28,6567-6584.
[162]S. W. J. Welch, Application of time-based fractional calculus methods to viscoelastic creep and stress relaxation of materials. Mech. Time-Depend Mat. 1999,3,279-303.
[163]M. Y. Xu, W. C. Tan, Representation of the constitutive equation of viscoelastic materials by the generalized fractional element networks and its generalized solutions, Science in China (Series G),2003,46 (2),145-157.
[164]S. Kempfle, Fractional calculus via functional calculus:theory and applications. Nonlinear Dynam.,2002,29,99-127.
[165]Y. Ding, Z. Wang, H. Ye, Optimal control of a fractional order HIV-immune system with memory, IEEE T. Contr. Syst. T.2012,20 (3),763-769.
[166]Y. Jiang, X. Wang, Y. Wang, On a stochastic heat equation with first order fractional noises and applications to finance, J. Math. Anal. Appl. in press.
[167]E. Kaslika, S. Sivasundaram, Nonlinear dynamics and chaos in fractional-order neural networks, Neural Networks,2012,32,245-256.
[168]J. He, Approximate analytical solution for seepage flow with fractional derivatives in porous media, Comput. Methods Appl. Mech. Engg.,1998,167, 57-68.
[169]D. Delbosco, L. Rodino, Existence and uniqueness for a nonlinear fractional differential equation, J. Math. Anal. Appl.,1996,204,609-625.
[170]D. Wu, On the solution process for a stochastic fractional partial differential equation driven by space-time white noise, Statist. Probab. Lett.,2011,81, 1161-1172.
[171]Y. T. Su, K.T.Wong, K. P. Ho, Linear MMSE Estimation of Large Magnitude Symmetric Levy-Process Phase-Noise, IEEE T. Commun.,2010, 12(58),3369-3374.
[172]D. Song, Optimal integrated ordering and production policy in a supply chain with stochastic lead-time, processing-time, and demand, IEEE Trans. Autom. Control,2009,54 (9),2027-2041.
[173]D. Seo, H. Lee, Stationary waiting times in m-node tandem queues with production blocking, IEEE Trans. Automat. Control,2011,56 (4),958-961,
[174]M. Taheri, K. Navaie, M. Bastani, On the outage probability of SIR-based power-controlled DS-CDMA networks with spatial Poisson traffic, IEEE Trans. Veh. Technol.,2010,59 (1),499-506.
[175]Z. J. Jurek, Invariant measures under random integral mappings and marginal distributions of fractional Levy processes, Stat. Probabil. Lett.,2013,1(83), 177-183.
[176]M. Rockner, T. Zhang, Stochastic evolution equations of jump type: existence, uniqueness and large deviation principle. Potential Anal.2007,26, 255-279.
[177]Z. Hou, J. Bao, C. Yuan, Exponential stability of energy solutions to stochastic partial differential equations with variable delay and jumps. J. Math. Anal. Appl.,2010,366,44-54.
[178]J. Cui, L. Yan, X. Sun, Exponential stability for neutral stochastic partial differential equations with delays and Poisson jumps, Statist. Probab. Lett.,2011, 81,1970-1977.
[179]K. Shi, Y. Wang, On a stochastic fractional partial differential equation driven by a Levy space-time white noise, J. Math. Anal. Appl.,2010,364, 119-129.
[180]A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, in:North-Holland Mathematics Studies, vol. 204, Elsevier Science B.V., Amsterdam,2006.
[181]M.M. El-Borai, Some probability densities and fundamental solutions of fractional evolution equations, Chaos, SolItons and Fract.,2002,14,433-440.
[182]J. Wang, Y. Zhou, A class of fractional evolution equations and optimal controls, Nonlinear Anal.2011,12,262-272.
[183]F.Mainardi, P. Paradisi, and R. Gorenflo, Probability distributions generated by fractional diffusion equations, in:J. Kertesz, I. Kondor (Eds.), Econophysics: An Emerging Science, Kluwer, Dordrecht,2000.
[184]D. Applebaum, Levy Processes and Stochastic Calculus, Cambridge University Press,2004.
[185]D. Song, Optimal integrated ordering and production policy in a supply chain with stochastic lead-time, processing-time, and demand, IEEE Trans. Autom. Control,2009,54 (9),2027-2041.
[186]X. Mao, A. Matasov, and A. Piunovskiy, Stochastic differential delay equations with Markovian switching, Bernoulli,20006 (1),73-90.
[187]J. Wang, H. Wu, and H. Li, Stochastically exponential stability and stabilization of uncertain linear hyperbolic PDE systems with Markov jumping parameters, Automatica,2012,48,569-576.
[188]J. Feng, J. Lam, and Z. Shu, Stabilization of Markovian systems via probability rate synthesis and output feedback, IEEE Trans. Automat. Control, 2010,55(3),773-777.
[189]M. Tanelli, B. Picasso, P. Bolzern, and P. Colaneri, Almost sure stabilization of uncertain continuous-Time Markov jump linear systems, IEEE Trans. Automat. Control,2010,55(1),195-201.
[190]X. Mao, Stability of stochastic differential equations with Markovian switching, Stochastic Process Appl.,1999,79,45-67.
[191]X. Mao, Exponential stability of stochastic delay interval systems with Markovian switching, IEEE Trans. Automat. Control,2002,47(10),1604-1612.
[192]S. Adlakha, S. Lall and A. Goldsmith, Networked Markov decision processes with delays, IEEE Trans. Automat. Control,2012,57(4),1013-1018.
[193]W. Li and Y. Jia, Consensus-based distributed multiple model UKF for jump Markov nonlinear systems, IEEE Trans. Automat. Control,2012,57(1),230-236,.
[194]J. W. Dong, Classical solutions to the one-dimensional stationary quantum drift-diffusion model, J. Math. Anal. Appl.,2013,399(2),594-598.
[195]D. Applebaum, Martingale-valued measures, Ornstein-Uhlenbeck processes with jumps and operator self-decomposability in Hilbert space, in:M. Emery, M. Yor (Eds.), Seminaire de Probabilities,2006,39, in:LNM, vol.1874, Springer, 171-197.
[196]D. Seo and H. Lee, Stationary waiting times in m-Node tandem queues with Production blocking, IEEE Trans. Automat. Control,2011,56(4),958-961.
[197]M. Taheri, K. Navaie, and M. Bastani, On the outage probability of SIR-based power-controlled DS-CDMA networks with spatial Poisson traffic, IEEE Trans. Veh. Technol.,2010,59(1),499-506.
[198]S. Peng and Y. Zhang, Some new criteria on pth moment stability of stochastic functional differential equations with markovian switching, IEEE Trans. Autom. Control,2010,55(12),2886-2890.
[199]S. Aihara, On adaptive boundary control for stochastic parabolic systems with unknown potential coefficient, IEEE Trans. Autom. Control,1997,42 (3), 350-363.
[200]J. Wang, B. Ren, and M. Krstic, Stabilization and gevrey regularity of a Schrodinger equation in boundary feedback with a heat equation, IEEE Trans. Autom. Control,2012,57 (1),179-185.
[201]A. K. Drame, D. Dochain, and J. J. Winkin, Asymptotic behavior and stability for solutions of a biochemical reactor distributed parameter Model, IEEE Trans. Autom. Control,2008,53(1),412-416.