模糊随机系统的分析和随机T-S模糊系统的控制
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摘要
随机性和模糊性是两种不同性质的不确定性，它们常常共存于系统中。由于他们涉及的数学工具不易结合，目前绝大多数系统分析和控制理论工作都只考虑用其中一种进行不确定性的建模，这样就造成一定的局限性。本文的目的是综合运用随机过程和模糊集合论的方法，通过更加精细地刻画系统不确定性，探索具有模糊随机不确定性的系统建模、分析和控制的新方法，并期望在最优性与鲁棒性之间寻求比较好的结合点。
当一个随机系统的输入或输出(观测)变量取值为模糊数，它就成为取值于模糊数空间上的随机系统，简称模糊随机系统。本文第一部分研究模糊随机系统的建模与分析的若干问题，推广了随机系统理论的一些结果。主要成果包括：提出了模糊随机变量协方差和反向协方差的概念；研究了二阶模糊随机变量的均方收敛性，并在此基础上得到了均方模糊随机分析、平稳模糊随机过程及其谱分解的若干定理；根据均方模糊随机分析理论，得到了输入为模糊随机过程的线性系统的输出输入统计特征关系方程；证明了Ito型模糊随机微分方程解的存在唯一性，并给出了Ito型线性模糊随机微分方程解的表达式，统计特征方程以及非线性模糊随机微分方程的数值解法；得到了模糊线性系统的稳定性和可观性条件、线性模糊随机系统统计特征方程和线性模糊随机系统的Kalman滤波算法；研究了当观测值是模糊数据时，线性回归模型的建立。
设控制对象是用Tag山一sugeno(T.s)模糊模型表示的非毕蜂琴攀{当
模型参姆到统计特征已知的瞰嗓杆扰吟一就成为一个瞬娜咚模
糊模型，本质上它是一个非线性随机微分系统。本文第二部分研彝雄舞
具有随机参数扰动的模糊系统稳定性分析和控制碱，将T，s_瞬娜事钾
控制理论的现有成果推广至随机T-s咖系终主要成果有二黄申了拿
葬摧
Randomness and fuzziness are two different kinds of uncertainty in complex systems. Since their mathematical tools are difficult to fuse, most of the known literature on system analysis and control considers only one of them to modeling the uncertainty, which results in some limitation. This dissertation is meant to combine the theory of stochastic processes and the theory of fuzzy sets to find some new methods of system modeling, analysis and control by describe uncertainty more minutely, and then to balance the optimization and the robustness.
If the input or output (observation) variables of a stochastic system are fuzzy, the system becomes a stochastic system on fuzzy number space, and is called a fuzzy stochastic system. The results in the dissertation cover various aspects of fuzzy stochastic systems, including the following: The notions of covariance and cross-covariance are introduced. The mean-square (m.s.) convergences of the sequence of fuzzy random variables are discussed, and then some theorems on m.s. fuzzy stochastic analysis and stationary fuzzy stochastic processes are proved. The equations of the mean value functions and the covariance functions are established for dynamical systems whose inputs are fuzzy stochastic processes. An existence and uniqueness theorem of Ito fuzzy stochastic differential equations is proved, some explicit representations of solutions and the equations of statistical characteristics are deduced for linear fuzzy stochastic differential equations, and numerical
methods to nonlinear fuzzy stochastic differential equations are proposed, The conditions for stability and observability of fuzzy linear systems are derived. The Kalman filter algorithms of linear fuzzy stochastic systems are brought forward. Moreover, the statistical linear regression with fuzzy observation data is discussed.
When the parameters of a Tagaki-Sugeno(T-S) fuzzy system are perturbed with random noise, the system turns to be a stochastic T-S system. Essentially, it is a nonlinear stochastic differential system. The second part of
the dissertation focuses on the stability analysis and control of the stochastic T-S systems. The main contributions include: The conditions of global m.s.
exponential stability, global almost surely (a,s.) exponential stability and
global robust exponential stability are constructed. A set of linear matrix inequality (LMI) conditions is proposed to guarantee the clossd-loop m.s. (energy) stability and a.s. (path) stability. Performance-oriented controller synthesis is also discussed and muti-objective controller can be designed based on it. LMI design methods for robust controller ,H controller and robust H, controller of the stochastic T-S systems with unmodeling uncertainties are introduced. Finally, various controllers developed in this dissertation are applied to Lorenz chaos system with random perturbations, and compared with traditional controllers. All me analysis and controller designs are based on LMIs, that are facile to be solved by Matlab software
当一个随机系统的输入或输出(观测)变量取值为模糊数，它就成为取值于模糊数空间上的随机系统，简称模糊随机系统。本文第一部分研究模糊随机系统的建模与分析的若干问题，推广了随机系统理论的一些结果。主要成果包括：提出了模糊随机变量协方差和反向协方差的概念；研究了二阶模糊随机变量的均方收敛性，并在此基础上得到了均方模糊随机分析、平稳模糊随机过程及其谱分解的若干定理；根据均方模糊随机分析理论，得到了输入为模糊随机过程的线性系统的输出输入统计特征关系方程；证明了Ito型模糊随机微分方程解的存在唯一性，并给出了Ito型线性模糊随机微分方程解的表达式，统计特征方程以及非线性模糊随机微分方程的数值解法；得到了模糊线性系统的稳定性和可观性条件、线性模糊随机系统统计特征方程和线性模糊随机系统的Kalman滤波算法；研究了当观测值是模糊数据时，线性回归模型的建立。
设控制对象是用Tag山一sugeno(T.s)模糊模型表示的非毕蜂琴攀{当
模型参姆到统计特征已知的瞰嗓杆扰吟一就成为一个瞬娜咚模
糊模型，本质上它是一个非线性随机微分系统。本文第二部分研彝雄舞
具有随机参数扰动的模糊系统稳定性分析和控制碱，将T，s_瞬娜事钾
控制理论的现有成果推广至随机T-s咖系终主要成果有二黄申了拿
葬摧
Randomness and fuzziness are two different kinds of uncertainty in complex systems. Since their mathematical tools are difficult to fuse, most of the known literature on system analysis and control considers only one of them to modeling the uncertainty, which results in some limitation. This dissertation is meant to combine the theory of stochastic processes and the theory of fuzzy sets to find some new methods of system modeling, analysis and control by describe uncertainty more minutely, and then to balance the optimization and the robustness.
If the input or output (observation) variables of a stochastic system are fuzzy, the system becomes a stochastic system on fuzzy number space, and is called a fuzzy stochastic system. The results in the dissertation cover various aspects of fuzzy stochastic systems, including the following: The notions of covariance and cross-covariance are introduced. The mean-square (m.s.) convergences of the sequence of fuzzy random variables are discussed, and then some theorems on m.s. fuzzy stochastic analysis and stationary fuzzy stochastic processes are proved. The equations of the mean value functions and the covariance functions are established for dynamical systems whose inputs are fuzzy stochastic processes. An existence and uniqueness theorem of Ito fuzzy stochastic differential equations is proved, some explicit representations of solutions and the equations of statistical characteristics are deduced for linear fuzzy stochastic differential equations, and numerical
methods to nonlinear fuzzy stochastic differential equations are proposed, The conditions for stability and observability of fuzzy linear systems are derived. The Kalman filter algorithms of linear fuzzy stochastic systems are brought forward. Moreover, the statistical linear regression with fuzzy observation data is discussed.
When the parameters of a Tagaki-Sugeno(T-S) fuzzy system are perturbed with random noise, the system turns to be a stochastic T-S system. Essentially, it is a nonlinear stochastic differential system. The second part of
the dissertation focuses on the stability analysis and control of the stochastic T-S systems. The main contributions include: The conditions of global m.s.
exponential stability, global almost surely (a,s.) exponential stability and
global robust exponential stability are constructed. A set of linear matrix inequality (LMI) conditions is proposed to guarantee the clossd-loop m.s. (energy) stability and a.s. (path) stability. Performance-oriented controller synthesis is also discussed and muti-objective controller can be designed based on it. LMI design methods for robust controller ,H controller and robust H, controller of the stochastic T-S systems with unmodeling uncertainties are introduced. Finally, various controllers developed in this dissertation are applied to Lorenz chaos system with random perturbations, and compared with traditional controllers. All me analysis and controller designs are based on LMIs, that are facile to be solved by Matlab software
引文
[1] L. Arnold, H. Crauel, V. Wihstutz, Stabilization of linear systems by noise, SIAM J. Control and Optimization 21 (1983) 451-461.
[2] K. J. Astrom, Introduction to Stochastic Control Theory, Academic Press, New York, 1970.
[3] J. P. Aubin, Differential inclusions, Springer-Verlag, 1984.
[4] J. Bondia, J. Pico, Analysis of linear systems with fuzzy parametric uncertainty, Fuzzy Sets andSystems 135(2003) 81-121
[5] S. B. Boswell, M. S. Taylor, A central limit theorem for fuzzy random variables, Fuzzy Sets and Systems, 24(1987), 331-344.
[6] A. E. Bouhtouri, D. Hirtrichsen, A. J. Pritchard, H~∞-type control for discrete-time stochastic systems, Inter. J Robust nonlinear control, 9(1999) 923-948.
[7] J.J. Buckley, T. Feuring, Comments on "Frequency/time domain methods for solutions of N-order fuzzy differential equations" by Zhang, Wang and Liu, Fuzzy Sets and Systems, 105(1999) 185-186.
[8] S. G. Cao, N. W. Rees, G. Feng, Quadratic stability analysis and design of continuous-time fuzzy control systems, lnter. J Systems Science, 27(1996)193-203.
[9] W. Chang, J. B. Park, Y. H. Joo, G.Chen, Design of robust fuzzy model based controller with sliding mode control for SISO nonlinear systems, Fuzzy sets and systems, 125(2002) 1-22.
[10] W. J. Chang, C. C. Shing, Extending covariance control for a class of discrete fuzzy stochastic systems, Proc. IEEE Conf Fuzzy systems, 2002,
558-563.
[11] W. J. Chang, S. M. Wu, Upper bound covariance control for continuous fuzzy stochastic systems with structured perturbations, Proc. IEEE Conf. Fuzzy systems, 2002, 92-97.
[12] B. S. Chen, C. S. Tseng, H. J. Uang, Robustness design of nonlinear dynamic systems via fuzzy linear control, IEEE Trans Fuzzy systems, 7(1999) 571- 585.
[13] B. S. Chen, C. S. Tseng, H. J. Uang, Mixed H_2/H_∞ fuzzy output feedback control design for nonlinear dynamic systems: an LMI approach, IEEE Trans Fuzzy systems, 8(2000)249- 265.
[14] B. S. Chen, C. S. Tseng, H. J Uang, Fuzzy differential games for nonlinear stochastic systems: suboptimal approach, IEEE Trans on Fuzzy Systems, 10(2002) 222-233.
[15] G Chen, J. Wang, L.S. Shieh, Interval Kalman filtering, IEEE Trans. Aerospace and Electronic systems, 33(1997) 250-259.
[16] G. Chen, Q. Xie and L.S. Shieh, Fuzzy Kalman filtering, Information Sciences 109(1998) 197-229.
[17] A. Colubi etal, On the formalization of fuzzy random variables, Information Sciences 133 (2001) 3-6.
[18] P. Diamond, Fuzzy least squares, Information Sciences, 46 (1988) 141-157.
[19] P. Diamond and P. Kloeden, Metrics space of fuzzy sets,Fuzzy Sets and Systems 35(1990) 241-249.
[20] P. Diamond, Brief note on the variation of constants formula for fuzzy differential equations, Fuzzy Sets and Systems 129(2002) 65-71.
[21] M. L.Diaz, Constructive definitions of fuzzy random variables, Stat. Prob. Letters, 36 (1997)135-143.
[22] M. L.Diaz, The λ-average value and the fuzzy expectation of fuzzy random variables, Fuzzy Sets and Systems, 99(1998) 347-352.
[23] M. L. Diaz, M. A. Gil, An extension of Fubuni's theorem for fuzzy random variables, Information Sciences 115(1999)29-41.
[24] Z. Ding, M. Ma, A. Kandel, Onthe observability of fuzzy dynamical control systems (Ⅰ), Fuzzy Sets and Systems, 111(2000) 225-236.
[25] Z. Ding and A. Kandel, On the observability of fuzzy dynamical control systems (Ⅱ), Fuzzy Sets and Systems 115 (2) (2000) pp. 261-277
[26] W. Dong, H.C. Shah, Vertex method for computing functions of fuzzy variables, Fuzzy Sets and Systems, 21 (1987) 183-199.
[27] C. Elkan, The paradoxical success of fuzzy logic, IEEE Expert, (1994) 3-8
[28] Y. Feng, Mean-square integral and differential of fuzzy stochastic processes, Fuzzy Sets and Systems 102(1999)271-280.
[29] Y. Feng, Convergence theorems for fuzzy random variables and fuzzy martingales, Fuzzy Sets and Systems 103(1999) 435-441.
[30] Y. Feng, Decomposition theorems for fuzzy supermartingales and submartingales, Fuzzy Sets and Systems 116 (2000) pp. 225-235
[31] Y. Feng, Fuzzy stochastic differential systems, Fuzzy Sets and Systems 115 (2000) 351-363
[32] Y. Feng, Mean-square Riemann-Stieltjes integrals of fuzzy stochastic processes and their applications, Fuzzy Sets and Systems 110 (2000) 27-41
[33] Y. Feng, Gaussian fuzzy random variables, Fuzzy Sets and Systems 111 (2000) 325-330
[34] Y. Feng, Fuzzy-valued mappings with finite variation, fuzzy-valued measures and fuzzy-valued Lebesgue-Stieltjes integrals, Fuzzy Sets and
Systems 121 (2001) 227-236
[35] Y. Feng, Sums of independent fuzzy random variables, Fuzzy Sets and Systems 123 (2001) 11-18
[36] Y. Feng, On the convergence of fuzzy martingales, Fuzzy Sets and Systems 130 (1) (2002) pp. 67-73
[37] Y. Feng, An approach to generalize laws of large numbers for fuzzy random variables, Fuzzy Sets and Systems 128 (2002) 237-245
[38] Y. Feng, Liangjian Hu and Huisheng Shu, The variance and covariance of fuzzy random variables and their applications, Fuzzy Sets and Systems 120 (2001) 487-497
[39] P. Ferrari and M. Savoia, Fuzzy number theory to obtain conservative results with respect to probability, Comput. Methods Appl. Mech. Eng. 160( 1998)205-222.
[40] A．Friedman，随机微分方程及其应用，吴让泉译，科学出版社，1983。
[41] M. Friedman, M. Ma, A. Kandel, Fuzzy linear systems, Fuzzy Sets and Systems, 96(1998)201-209.
[42] T. Fukuda and Y. Sunahara, Identification of vaguely parameters for a class of fuzzy stochastic systems, Proc. IEEE Conf. Fuzzy Systems (1992) 1419-1426.
[43] D. Garcia, M. A. Lubiano, M .C. Alonso, Estimating the expected value of fuzzy random variables in the stratified random sampling from finite populations, Information Sciences 138(2001) 165-184.
[44] G.Z. Gertner and H. Zhu, Bayesian estimation in forest surveys when samples or prior information are fuzzy, Fuzzy Sets and Systems 77(1996)277-290.
[45] L. Ghaoui, State-feedback control of systems with multiplicative noise via linear matrix inequalities, System & Control Letters 24(1995)
223-228.
[46] M.A. Gil and P. Jain, Comparison of experiments in statistical decision problems with fuzzy utilities, IEEE Trans. SMC, 22 (1992) 662-670.
[47] T. M. Guerra, and L. Vermeiren, Control laws for Takagi - Sugeno fuzzy models, Fuzzy Sets and Systems 120(2001)95-108.
[48] M. Hanss, The transformation method for the simulation and analysis of systems with uncertain parameters, Fuzzy Sets and Systems, 130(2002) 277-289.
[49] D. Hinrichsen, A. J. Pritchard, Stochastic H~∞, SIAM J. Control Optim, 36(1998) 1504-1538.
[50] L. Hong and G. J. Wang, Centralized integration ofmultisensor noisy and fuzzy data, IEE Proc. Control Theory Appl. 142(1995)459-465.
[51] S. K. Hong, R. Langari, An LMI-based fuzzy H~∞ control system design with TS framework, Information Sciences, 123(2000) 163-179.
[52] L. Hu, R. Wu, S. Shao, Analysis of dynamical systems whose inputs are fuzzy stochastic processes, Fuzzy Sets and Systems, 129(2002) 111 - 118
[53] C. Hwang and J. Yao, Independent fuzzy random variables and their application, Fuzzy Sets and Systems 82 (1996) 335-350.
[54] C.M. Hwang, A theorem of renewal process for fuzzy random variables and its application, Fuzzy Sets and Systems 116 (2000) 237-244.
[55] H. Inoue, Randomly weighted sums of exchangeable fuzzy random variables, Fuzzy Sets and Systems 69(1995) 347-354.
[56] B. K. Kim, J. H. Kim, Stochastic integrals of Set-valued processes and fuzzy processes, J. Math. Anal. Appl.236 (1999) 480-502.
[57] E. Kim, H. Lee, New approaches to relaxed quadratic stability condition of fuzzy control systems, IEEE Trans on Fuzzy Systems, 8 (2000)
523-533.
[58] K. Kim, J. Joh, R. Langari, W. Kwon, LMI-Based design of Takagi-Sugeno Fuzzy Controllers for nonlinear dynamic systems using fuzzy estimators, Inter. J. Fuzzy systems, 1(2) 133-144.
[59] E.P. Klement, M.L. Puri, D.A. Ralescu, Limit theorems for fuzzy random variables, Proc. Roy. Soc. London(Ser. A) 407(1986) 171-182.
[60] G. J. Klir, Constrained fuzzy arithmetic: basic questions and some answers, Soft Computing 2(1998) 100-108.
[61] P.E. Kloeden, E. Platen, Numerical Solution of Stochastic Differential Equations, Springer-Verlag, 1992.
[62] R. Komer, On the variance of fuzzy random variables, Fuzzy Sets and Systems 92(1997) 83-93.
[63] R. Komer, An asymptotic α-test for the expectation of random fuzzy variables, Journal of Statistical Planning and Inference, 83(2000) 331-346.
[64] R. Komer, W. Nather, Linear regression with random fuzzy variables: extended classical estimates, best linear estimates, least squares estimates, Information Sciences 109(1998) 95-118.
[65] V. Kratschmer, Constraints of belief function by fuzzy random variables, IEEE Trans SMC(B) 28(1998)881-883.
[66] V. Kratschmer, A unified approach to fuzzy random variables, Fuzzy Sets and Systems 123(2001) 1-9.
[67] R. Kruse, The strong law of large numbers for fuzzy random variables, Information Sciences 28(1982)233-241.
[68] R. Kruse, On the variance of random sets, J Math. Anal. Appl. 122(I987) 469-473.
[69] R. Kruse, K.D. Meyer, Statistics with vague data, Reidel,Dordrecht,
Boston, 1987.
[70] H. Kwarkernaak, Fuzzy random variables Ⅰ, Information Sciences 15 (1978) 1-29. Ⅱ, Information Sciences 17 (1979) 253-278.
[71] J. R. Layne, K.M. Passino, A fuzzy dynamic model based state estimator, Fuzzy Sets and Systems 122(2001) 45-72.
[72] H. J. Lee, J. B. Park, G. Chen, Robust fuzzy control of nonlinear systems with parametric uncertainties, IEEE Trans Fuzzy systems 9(2001) 369-379.
[73] K. R. Lee, E. T. Jeung and H. B. Park, Robust fuzzy H~∞ control for uncertain nonlinear systems via state feedback: an LMI approach, Fuzzy Sets andSystems 120 (2001) 123-134
[74] R. P. Leland, Fuzzy differential systems and Malliavin calculus, Fuzzy Sets and Systems 70 (1995) 59-73
[75] R. P. Leland, Feedback linearization control design for systems with fuzzy uncertainty, IEEE Trans Fuzzy systems 8(1998) 492-503.
[76] J. Li, etal. A fuzzy logic approach to optimal control of nonlinear systems, Inter. J. Fuzzy systems, 2(2000) 153-163.
[77] S. Li, Y Ogura, V Kreinovich, Limit theorems and Applications of set-valued and fuzzy set-valued random variables, Kluwer, to appear
[78] P. Liu, Fuzzy-valued Markov processes and their properties, Fuzzy Sets and Systems 91(1997) 45-52.
[79] Y. Liu, Z. Qiao and G. Wang, Fuzzy random reliability of structures based on Fuzzy random variables, Fuzzy Sets and Systems 86(1997)345-355.
[80] M.K. Luhandjula, Fuzziness and randomness in an optimization framework, Fuzzy Sets and Systems 77 (1996) 291-297.
[81] M.K. Luhandjula, M.M. Gupta, On fuzzy stochastic optimization, Fuzzy
Sets and Systems 81(I996), 47-55.
[82] X. J. Ma, Z. Q. Sun, Y. Y. He, Analysis and design of fuzzy controller and fuzzy observer, IEEE Trans Fuzzy systems, 6 (1998) 41- 51.
[83] M. Ma, M. Friedman, A. Kandel, Numerical solutions of fuzzy differential equations, Fuzzy Sets and Systems 105(1999) 133-138.
[84] X. Mao, Exponential Stability of Stochastic Differential Equations. Marcel Dekker, 1994.
[85] X. Mao, Stochastic stabilization and destabilization, System & Control letters 23(1994)279-290.
[86] X. Mao, C. Selfridge, Stability of stochastic interval systems with time delays, System & Control Letters 42(2001) 279-290.
[87] M. Montenegro, M. R. Casals, M. A. Lubiano, M .A. Gil, Two-sample hypothesis tests of means of a fuzzy random variable,Information Sciences 133(2001)89-100.
[88] W. Nather. Linear statistucal inference for random fuzzy data. Statistics, 29 (1997) 221-240.
[89] H. T. Nguyen, A note on the extension principle for fuzzy sets, J. Math. Anal. Appl. 64(1978)369-380.
[90] H. T. Nguyen, A empirical study on robustness of fuzzy logic, Proceeding of Conference on Fuzzy System, 1993, 543-47.
[91] H.T. Nguyen, How stable is a fuzzy linear system?, Proceeding IEEE Conf Fuzzy Systems (1994) 1023-1027.
[92] H.T. Nguyen, Fuzzy sets and probability, Fuzzy Sets and Systems 90 (1997) 129-132.
[93] V. A. Niskanen, Prospects for soft statistical computing: describing data and inferring from data with words in the Human Sciences, Sciences 132 (2001) 83-131
[94] B. Okesendal, Stochastic differential equations: An introduction with applications, Springer-Verlag, 1998
[95] C.W. Park, C. H. Lee and M. Park, Design of an adaptive fuzzy model based controller for chaotic dynamics in Lorenz systems with uncertainty, Information Sciences 147 (2002) 245-266
[96] C. W. Park, LMI-based robust stability analysis for fuzzy feedback linearization regulators with its applications, Information Sciences, 152(2003) 287-301.
[97] F. N. Proske and M. L. Puri, Strong law of large numbers for Banach space valued fuzzy random variables, Journal of Theoretical Probability, 15(2002) 543-551.
[98] M.L. Puri and D.A. Ralescu, The concept of normality for fuzzy random variables, The Annals of Prob. 13 (1985) 1373-1379.
[99] M.L. Puri and D.A. Ralescu, Fuzzy random variables, J Math. Anal Appl. 114(1986) 409-422.
[100] M.L. Puri and D.A. Ralescu, Convergence theorem for fuzzy martingales, J. Math. Anal, Appl. 160 (1991) 107-122.
[101] Z. Qiao and G. Wang, On solutions and distribution problems of the linear programming with fuzzy random variable coefficients, Fuzzy Sets and Systems 58(1993) 155-170.
[102] D. A. Ralescu, Fuzzy random variables revisited, Proceeding IEEE Conf Fuzzy Systems, 2 (1995) 993-1000.
[103] C. Romer and A. Kandel, Constraints on belief functions imposed by fuzzy random variables, IEEE Trans. SMC 25(1995) 86-99.
[104] S. Schnatter, Linear dynamic systems and fuzzy data, in: Trapple R. (Eds.)Cybernetics and Systems, 1990, pp 147-154.
[105] S. Schnatter, On statistical inference for fuzzy data with applications to descriptive statistics, Fuzzy Sets andSystems 50(t992) 143-156.
[106] Q. Song, R. P. Leland and B. S. Chissom, Fuzzy stochastic fuzzy time series and its models, Fuzzy Sets andSystems 88 (1997) 333-341
[107] M.Stojakovic, Fuzzy random variable expectation and martingale, J. Math. Anal. Appl. 184 (1994) 594-616.
[108] H. Tanaka, Fuzzy data analysis by possibility linear models,Fuzzy Sets and Systems 24(1987) 363-375.
[109] K. Tanaka, T. Ikeda, H. O. Wang, Fuzzy Regulators and fuzzy observers: relaxed stability conditions and LMI-based designs, IEEE Trans on Fuzzy Systems 6 (1998) 250-265.
[110] K. Tanaka, T. Ikeda, H. O. Wang, Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: Quadric stability, H~∞ control theory, and Linear Matrix Inequalities, IEEE Trans on Fuzzy Systems 8 (2000) 1-12.
[111] K. Tanaka, M. Sugeno, Stability analysis and design of fuzzy control systems, Fuzzy Sets and Systems 45(1992) 135-156.
[112] T. Taniguchi, K. Tanaka, H. Ohtake, H .O. Wang, Model construction, rule reduction, and robust compensation for generalized form of Takagi-Sugeno fuzzy systems, IEEE Trams Fuzzy systems,9(2001) 525-538.
[113] D. Vorobiev, S. Seikkala, Towards the theory of fuzzy differential equations, Fuzzy Sets and Systems 125 (2002) 231-237.
[114] G, Wang and Y. Zhang, The theory of fuzzy stochastic processes,Fuzzy Sets and Systems 51(1992)161-178.
[115] G Wang and Z. Qiao, Convergence of sequences of fuzzy random variables and its application, Fuzzy Sets and Systems 63(1994) 187-199,
[116] H. O. Wang, K. Tanaka, M. F. Griffin, An Approach to fuzzy control of nonlinear systems: stability and design issues, IEEE Trans on Fuzzy Systems 4 (1996) 14-23.
[117] L.X. Wang, Stable adaptive fuzzy controllers with application to inverted pendulum tracking, IEEE Trans. on SMC-Part B, V26, No5, 1996.
[118] Z. Wang, D. W. C. Ho, K. J. Burnham, Robust stability of uncertain stochastic fuzzy systems with time-delays, Technical correspondence. 2002.
[119] H.C. Wu, The central limit theorems for fuzzy random variables, Information Sciences 120 (1999) 239-256.
[120] S. J. Wu, C. T. Lin, Optimal fuzzy controller design in continuous fuzzy system: Global concept approach, IEEE Trans Fuzzy systems 8(2000) 713-729.
[121] S. J. Wu, C .T. Lin, Global optimal fuzzy tracker design based on local concept approach, IEEE Trans Fuzzy systems, 10(2002) 128- 143.
[122] S. Xu, T. Chen, Robust H_∞ control for uncertain stochastic systems with state delay, IEEE Trans Automatic Control 47(2002) 2089-2094.
[123] F. Yang, Z. Wang, Y. S Hung, Robust Kalman filtering for discrete time-varying uncertain systems with multiplicative noises, IEEE Trans Automatic Control 47(2002) 1179-1183.
[124] M. S. Yang, T. S. Lin, Fuzzy least-squares linear regression analysis for fuzzy input-output data, Fuzzy Sets and Systems 126(2002) 389-399.
[125] Y. Yosida, etal., Optimal stopping problems in a stochastic and fuzzy system, J. Math Anal. Appl. 246(2000) 135-149.
[126] Y. Yosida, The valuation of European options in uncertain envionment,
European J. Operational Research 145(2003)221-229.
[127] L.A.Zadeh, Fuzzy logic = computing with words, IEEE Trans. on Fuzzy Systems, 4(1996) 103-110.
[128] P. Zeephongsekul and G. Xia, On fuzzy debugging of software programs, Fuzzy Sets and Systems 83(1996)239 - 247.
[129] Y. Zhang, G. Wang and F. Su, The general theory for response analysis of fuzzy stochastic dynamical systems, Fuzzy Sets and Systems 83(1996)369-405.
[130] C. Zhong and G. Zhou, The equivalence of two definition of fuzzy random variables. Preprints of 2nd IFSA Congress, (1987)59-62.
[131] S. Zhou and G. Feng, Comment on "Optimal Fuzzy Controller Design: Local Concept Approach", IEEE Trans Fuzzy systems, 11(2003) 279-280
[132] Z. Zmeskal, Application of the fuzzy-stochastic methodology to appraising the firm value as a European call option, European Journal of Operational Research, 135 (2001) 303-310
[133] 丁永生，应浩，任立红，邵世煌，解析模糊控制理论：模糊控制系统的结构和稳定性分析，控制与决策，2000，15(2)：29-135．
[134] 冯玉瑚，模糊随机微分方程，中国纺织大学学报，1999，25(1)82-86．
[135] 郭尚来，随机控制，清华大学出版社，1999。
[136] 哈明虎，王光远，连续时间模糊随机系统分析—状态空间模型分析， 哈尔滨建筑大学学报，30(5)，1992：1-10．
[137] 韩崇昭，王月娟，万百五，随机系统理论，西安交通大学出版社，西安，1987。
[138] 胡良剑，吴让泉．模糊随机变量的均方收敛性，中国纺织大学学报， 1998，24(5)：57-60
[139] 雷耀斌，吴让泉．模糊随机系统的卡尔曼滤波，中国纺织大学学报， 1998，24(3)：79-82
[140] 李寿梅，关于Fuzzy随机变量的进一步讨论，河北大学学报，1990，10(4)：8-13．
[141] 廖晓昕，动力系统稳定性理论和应用，北京：国防工业出版社，2000．
[142] 刘晓东，张庆灵，王岩， 基于LMI的T-S模糊系统的H_∞控制，控制与决策，2002，17(6)：924-927．
[143] 欧进萍，吴波，王光远，模糊随机过程与模糊随机微分方程的解法， 哈尔滨建筑工程学院学报，25卷1期(1992)1-10．
[144] 汤兵勇，模糊大系统的自适应协调控制算法，中国控制会议论文集， 1995．
[145] 冯纯伯，田玉平，忻欣，鲁棒控制系统设计，东南大学出版社，1995。
[146] 王光远，乔忠，随机线性规划的单纯形法与模糊随机线性规划的解法，哈尔滨建筑工程学院学报，26卷6期(1993)1-6．
[147] 王立新，模糊系统：挑战与机遇并存．十年研究之感悟，自动化学报， 2001，27(4)：585-590．
[148] 吴从忻，马明，方锦暄．模糊分析学的结构理论．贵州科技出版社， 1994
[149] 吴从忻，马明．模糊分析学基础．国防工业出版社，1991
[150] 吴让泉，胡良剑．二阶模糊随机过程的均方收敛性及其应用．数理 统计与应用概率，1998，13(3)：175-182
[151] 谢立，何星，张卫东，许晓鸣，非线性不确定随机多重时滞系统的
鲁棒H_∞控制，控制与决策，2001，16(增刊)：779-786．
[152] 应浩，关于模糊控制理论与应用的若干问题，自动化学报，2001， 27(4)：591-592．
[153] 俞立，鲁棒控制——线性矩阵不等式方法，清华大学出版社，2002。
[154] 张炳根，赵玉芝．科学与工程中的随机微分方程．海洋出版社，1980。
[155] 张继国，张文修，模糊随机变量及其概率分布，模糊系统与数学， 1996，lO(4)：76-82．
[156] 张世英，王东，基金投资行为及其监管的模糊随机理论研究，管理科学学报，2000，3(1)：58-65． _
[157] 张文修，刘道远，随机F集及其性质，模糊系统与数学，1990,：4(2)1-9．
[158] 张跃，王光远．模糊随机动力系统理论．科学出版社，1993
[159] 周克敏，J．C．Doyle，K．Glover,鲁棒与最优控制，北京：国防工业出版社，2002．
[160] 周智，于朝霞，模糊随机变量的数字特征，模糊系统与数学，1990，4(1)．49-54．
[2] K. J. Astrom, Introduction to Stochastic Control Theory, Academic Press, New York, 1970.
[3] J. P. Aubin, Differential inclusions, Springer-Verlag, 1984.
[4] J. Bondia, J. Pico, Analysis of linear systems with fuzzy parametric uncertainty, Fuzzy Sets andSystems 135(2003) 81-121
[5] S. B. Boswell, M. S. Taylor, A central limit theorem for fuzzy random variables, Fuzzy Sets and Systems, 24(1987), 331-344.
[6] A. E. Bouhtouri, D. Hirtrichsen, A. J. Pritchard, H~∞-type control for discrete-time stochastic systems, Inter. J Robust nonlinear control, 9(1999) 923-948.
[7] J.J. Buckley, T. Feuring, Comments on "Frequency/time domain methods for solutions of N-order fuzzy differential equations" by Zhang, Wang and Liu, Fuzzy Sets and Systems, 105(1999) 185-186.
[8] S. G. Cao, N. W. Rees, G. Feng, Quadratic stability analysis and design of continuous-time fuzzy control systems, lnter. J Systems Science, 27(1996)193-203.
[9] W. Chang, J. B. Park, Y. H. Joo, G.Chen, Design of robust fuzzy model based controller with sliding mode control for SISO nonlinear systems, Fuzzy sets and systems, 125(2002) 1-22.
[10] W. J. Chang, C. C. Shing, Extending covariance control for a class of discrete fuzzy stochastic systems, Proc. IEEE Conf Fuzzy systems, 2002,
558-563.
[11] W. J. Chang, S. M. Wu, Upper bound covariance control for continuous fuzzy stochastic systems with structured perturbations, Proc. IEEE Conf. Fuzzy systems, 2002, 92-97.
[12] B. S. Chen, C. S. Tseng, H. J. Uang, Robustness design of nonlinear dynamic systems via fuzzy linear control, IEEE Trans Fuzzy systems, 7(1999) 571- 585.
[13] B. S. Chen, C. S. Tseng, H. J. Uang, Mixed H_2/H_∞ fuzzy output feedback control design for nonlinear dynamic systems: an LMI approach, IEEE Trans Fuzzy systems, 8(2000)249- 265.
[14] B. S. Chen, C. S. Tseng, H. J Uang, Fuzzy differential games for nonlinear stochastic systems: suboptimal approach, IEEE Trans on Fuzzy Systems, 10(2002) 222-233.
[15] G Chen, J. Wang, L.S. Shieh, Interval Kalman filtering, IEEE Trans. Aerospace and Electronic systems, 33(1997) 250-259.
[16] G. Chen, Q. Xie and L.S. Shieh, Fuzzy Kalman filtering, Information Sciences 109(1998) 197-229.
[17] A. Colubi etal, On the formalization of fuzzy random variables, Information Sciences 133 (2001) 3-6.
[18] P. Diamond, Fuzzy least squares, Information Sciences, 46 (1988) 141-157.
[19] P. Diamond and P. Kloeden, Metrics space of fuzzy sets,Fuzzy Sets and Systems 35(1990) 241-249.
[20] P. Diamond, Brief note on the variation of constants formula for fuzzy differential equations, Fuzzy Sets and Systems 129(2002) 65-71.
[21] M. L.Diaz, Constructive definitions of fuzzy random variables, Stat. Prob. Letters, 36 (1997)135-143.
[22] M. L.Diaz, The λ-average value and the fuzzy expectation of fuzzy random variables, Fuzzy Sets and Systems, 99(1998) 347-352.
[23] M. L. Diaz, M. A. Gil, An extension of Fubuni's theorem for fuzzy random variables, Information Sciences 115(1999)29-41.
[24] Z. Ding, M. Ma, A. Kandel, Onthe observability of fuzzy dynamical control systems (Ⅰ), Fuzzy Sets and Systems, 111(2000) 225-236.
[25] Z. Ding and A. Kandel, On the observability of fuzzy dynamical control systems (Ⅱ), Fuzzy Sets and Systems 115 (2) (2000) pp. 261-277
[26] W. Dong, H.C. Shah, Vertex method for computing functions of fuzzy variables, Fuzzy Sets and Systems, 21 (1987) 183-199.
[27] C. Elkan, The paradoxical success of fuzzy logic, IEEE Expert, (1994) 3-8
[28] Y. Feng, Mean-square integral and differential of fuzzy stochastic processes, Fuzzy Sets and Systems 102(1999)271-280.
[29] Y. Feng, Convergence theorems for fuzzy random variables and fuzzy martingales, Fuzzy Sets and Systems 103(1999) 435-441.
[30] Y. Feng, Decomposition theorems for fuzzy supermartingales and submartingales, Fuzzy Sets and Systems 116 (2000) pp. 225-235
[31] Y. Feng, Fuzzy stochastic differential systems, Fuzzy Sets and Systems 115 (2000) 351-363
[32] Y. Feng, Mean-square Riemann-Stieltjes integrals of fuzzy stochastic processes and their applications, Fuzzy Sets and Systems 110 (2000) 27-41
[33] Y. Feng, Gaussian fuzzy random variables, Fuzzy Sets and Systems 111 (2000) 325-330
[34] Y. Feng, Fuzzy-valued mappings with finite variation, fuzzy-valued measures and fuzzy-valued Lebesgue-Stieltjes integrals, Fuzzy Sets and
Systems 121 (2001) 227-236
[35] Y. Feng, Sums of independent fuzzy random variables, Fuzzy Sets and Systems 123 (2001) 11-18
[36] Y. Feng, On the convergence of fuzzy martingales, Fuzzy Sets and Systems 130 (1) (2002) pp. 67-73
[37] Y. Feng, An approach to generalize laws of large numbers for fuzzy random variables, Fuzzy Sets and Systems 128 (2002) 237-245
[38] Y. Feng, Liangjian Hu and Huisheng Shu, The variance and covariance of fuzzy random variables and their applications, Fuzzy Sets and Systems 120 (2001) 487-497
[39] P. Ferrari and M. Savoia, Fuzzy number theory to obtain conservative results with respect to probability, Comput. Methods Appl. Mech. Eng. 160( 1998)205-222.
[40] A．Friedman，随机微分方程及其应用，吴让泉译，科学出版社，1983。
[41] M. Friedman, M. Ma, A. Kandel, Fuzzy linear systems, Fuzzy Sets and Systems, 96(1998)201-209.
[42] T. Fukuda and Y. Sunahara, Identification of vaguely parameters for a class of fuzzy stochastic systems, Proc. IEEE Conf. Fuzzy Systems (1992) 1419-1426.
[43] D. Garcia, M. A. Lubiano, M .C. Alonso, Estimating the expected value of fuzzy random variables in the stratified random sampling from finite populations, Information Sciences 138(2001) 165-184.
[44] G.Z. Gertner and H. Zhu, Bayesian estimation in forest surveys when samples or prior information are fuzzy, Fuzzy Sets and Systems 77(1996)277-290.
[45] L. Ghaoui, State-feedback control of systems with multiplicative noise via linear matrix inequalities, System & Control Letters 24(1995)
223-228.
[46] M.A. Gil and P. Jain, Comparison of experiments in statistical decision problems with fuzzy utilities, IEEE Trans. SMC, 22 (1992) 662-670.
[47] T. M. Guerra, and L. Vermeiren, Control laws for Takagi - Sugeno fuzzy models, Fuzzy Sets and Systems 120(2001)95-108.
[48] M. Hanss, The transformation method for the simulation and analysis of systems with uncertain parameters, Fuzzy Sets and Systems, 130(2002) 277-289.
[49] D. Hinrichsen, A. J. Pritchard, Stochastic H~∞, SIAM J. Control Optim, 36(1998) 1504-1538.
[50] L. Hong and G. J. Wang, Centralized integration ofmultisensor noisy and fuzzy data, IEE Proc. Control Theory Appl. 142(1995)459-465.
[51] S. K. Hong, R. Langari, An LMI-based fuzzy H~∞ control system design with TS framework, Information Sciences, 123(2000) 163-179.
[52] L. Hu, R. Wu, S. Shao, Analysis of dynamical systems whose inputs are fuzzy stochastic processes, Fuzzy Sets and Systems, 129(2002) 111 - 118
[53] C. Hwang and J. Yao, Independent fuzzy random variables and their application, Fuzzy Sets and Systems 82 (1996) 335-350.
[54] C.M. Hwang, A theorem of renewal process for fuzzy random variables and its application, Fuzzy Sets and Systems 116 (2000) 237-244.
[55] H. Inoue, Randomly weighted sums of exchangeable fuzzy random variables, Fuzzy Sets and Systems 69(1995) 347-354.
[56] B. K. Kim, J. H. Kim, Stochastic integrals of Set-valued processes and fuzzy processes, J. Math. Anal. Appl.236 (1999) 480-502.
[57] E. Kim, H. Lee, New approaches to relaxed quadratic stability condition of fuzzy control systems, IEEE Trans on Fuzzy Systems, 8 (2000)
523-533.
[58] K. Kim, J. Joh, R. Langari, W. Kwon, LMI-Based design of Takagi-Sugeno Fuzzy Controllers for nonlinear dynamic systems using fuzzy estimators, Inter. J. Fuzzy systems, 1(2) 133-144.
[59] E.P. Klement, M.L. Puri, D.A. Ralescu, Limit theorems for fuzzy random variables, Proc. Roy. Soc. London(Ser. A) 407(1986) 171-182.
[60] G. J. Klir, Constrained fuzzy arithmetic: basic questions and some answers, Soft Computing 2(1998) 100-108.
[61] P.E. Kloeden, E. Platen, Numerical Solution of Stochastic Differential Equations, Springer-Verlag, 1992.
[62] R. Komer, On the variance of fuzzy random variables, Fuzzy Sets and Systems 92(1997) 83-93.
[63] R. Komer, An asymptotic α-test for the expectation of random fuzzy variables, Journal of Statistical Planning and Inference, 83(2000) 331-346.
[64] R. Komer, W. Nather, Linear regression with random fuzzy variables: extended classical estimates, best linear estimates, least squares estimates, Information Sciences 109(1998) 95-118.
[65] V. Kratschmer, Constraints of belief function by fuzzy random variables, IEEE Trans SMC(B) 28(1998)881-883.
[66] V. Kratschmer, A unified approach to fuzzy random variables, Fuzzy Sets and Systems 123(2001) 1-9.
[67] R. Kruse, The strong law of large numbers for fuzzy random variables, Information Sciences 28(1982)233-241.
[68] R. Kruse, On the variance of random sets, J Math. Anal. Appl. 122(I987) 469-473.
[69] R. Kruse, K.D. Meyer, Statistics with vague data, Reidel,Dordrecht,
Boston, 1987.
[70] H. Kwarkernaak, Fuzzy random variables Ⅰ, Information Sciences 15 (1978) 1-29. Ⅱ, Information Sciences 17 (1979) 253-278.
[71] J. R. Layne, K.M. Passino, A fuzzy dynamic model based state estimator, Fuzzy Sets and Systems 122(2001) 45-72.
[72] H. J. Lee, J. B. Park, G. Chen, Robust fuzzy control of nonlinear systems with parametric uncertainties, IEEE Trans Fuzzy systems 9(2001) 369-379.
[73] K. R. Lee, E. T. Jeung and H. B. Park, Robust fuzzy H~∞ control for uncertain nonlinear systems via state feedback: an LMI approach, Fuzzy Sets andSystems 120 (2001) 123-134
[74] R. P. Leland, Fuzzy differential systems and Malliavin calculus, Fuzzy Sets and Systems 70 (1995) 59-73
[75] R. P. Leland, Feedback linearization control design for systems with fuzzy uncertainty, IEEE Trans Fuzzy systems 8(1998) 492-503.
[76] J. Li, etal. A fuzzy logic approach to optimal control of nonlinear systems, Inter. J. Fuzzy systems, 2(2000) 153-163.
[77] S. Li, Y Ogura, V Kreinovich, Limit theorems and Applications of set-valued and fuzzy set-valued random variables, Kluwer, to appear
[78] P. Liu, Fuzzy-valued Markov processes and their properties, Fuzzy Sets and Systems 91(1997) 45-52.
[79] Y. Liu, Z. Qiao and G. Wang, Fuzzy random reliability of structures based on Fuzzy random variables, Fuzzy Sets and Systems 86(1997)345-355.
[80] M.K. Luhandjula, Fuzziness and randomness in an optimization framework, Fuzzy Sets and Systems 77 (1996) 291-297.
[81] M.K. Luhandjula, M.M. Gupta, On fuzzy stochastic optimization, Fuzzy
Sets and Systems 81(I996), 47-55.
[82] X. J. Ma, Z. Q. Sun, Y. Y. He, Analysis and design of fuzzy controller and fuzzy observer, IEEE Trans Fuzzy systems, 6 (1998) 41- 51.
[83] M. Ma, M. Friedman, A. Kandel, Numerical solutions of fuzzy differential equations, Fuzzy Sets and Systems 105(1999) 133-138.
[84] X. Mao, Exponential Stability of Stochastic Differential Equations. Marcel Dekker, 1994.
[85] X. Mao, Stochastic stabilization and destabilization, System & Control letters 23(1994)279-290.
[86] X. Mao, C. Selfridge, Stability of stochastic interval systems with time delays, System & Control Letters 42(2001) 279-290.
[87] M. Montenegro, M. R. Casals, M. A. Lubiano, M .A. Gil, Two-sample hypothesis tests of means of a fuzzy random variable,Information Sciences 133(2001)89-100.
[88] W. Nather. Linear statistucal inference for random fuzzy data. Statistics, 29 (1997) 221-240.
[89] H. T. Nguyen, A note on the extension principle for fuzzy sets, J. Math. Anal. Appl. 64(1978)369-380.
[90] H. T. Nguyen, A empirical study on robustness of fuzzy logic, Proceeding of Conference on Fuzzy System, 1993, 543-47.
[91] H.T. Nguyen, How stable is a fuzzy linear system?, Proceeding IEEE Conf Fuzzy Systems (1994) 1023-1027.
[92] H.T. Nguyen, Fuzzy sets and probability, Fuzzy Sets and Systems 90 (1997) 129-132.
[93] V. A. Niskanen, Prospects for soft statistical computing: describing data and inferring from data with words in the Human Sciences, Sciences 132 (2001) 83-131
[94] B. Okesendal, Stochastic differential equations: An introduction with applications, Springer-Verlag, 1998
[95] C.W. Park, C. H. Lee and M. Park, Design of an adaptive fuzzy model based controller for chaotic dynamics in Lorenz systems with uncertainty, Information Sciences 147 (2002) 245-266
[96] C. W. Park, LMI-based robust stability analysis for fuzzy feedback linearization regulators with its applications, Information Sciences, 152(2003) 287-301.
[97] F. N. Proske and M. L. Puri, Strong law of large numbers for Banach space valued fuzzy random variables, Journal of Theoretical Probability, 15(2002) 543-551.
[98] M.L. Puri and D.A. Ralescu, The concept of normality for fuzzy random variables, The Annals of Prob. 13 (1985) 1373-1379.
[99] M.L. Puri and D.A. Ralescu, Fuzzy random variables, J Math. Anal Appl. 114(1986) 409-422.
[100] M.L. Puri and D.A. Ralescu, Convergence theorem for fuzzy martingales, J. Math. Anal, Appl. 160 (1991) 107-122.
[101] Z. Qiao and G. Wang, On solutions and distribution problems of the linear programming with fuzzy random variable coefficients, Fuzzy Sets and Systems 58(1993) 155-170.
[102] D. A. Ralescu, Fuzzy random variables revisited, Proceeding IEEE Conf Fuzzy Systems, 2 (1995) 993-1000.
[103] C. Romer and A. Kandel, Constraints on belief functions imposed by fuzzy random variables, IEEE Trans. SMC 25(1995) 86-99.
[104] S. Schnatter, Linear dynamic systems and fuzzy data, in: Trapple R. (Eds.)Cybernetics and Systems, 1990, pp 147-154.
[105] S. Schnatter, On statistical inference for fuzzy data with applications to descriptive statistics, Fuzzy Sets andSystems 50(t992) 143-156.
[106] Q. Song, R. P. Leland and B. S. Chissom, Fuzzy stochastic fuzzy time series and its models, Fuzzy Sets andSystems 88 (1997) 333-341
[107] M.Stojakovic, Fuzzy random variable expectation and martingale, J. Math. Anal. Appl. 184 (1994) 594-616.
[108] H. Tanaka, Fuzzy data analysis by possibility linear models,Fuzzy Sets and Systems 24(1987) 363-375.
[109] K. Tanaka, T. Ikeda, H. O. Wang, Fuzzy Regulators and fuzzy observers: relaxed stability conditions and LMI-based designs, IEEE Trans on Fuzzy Systems 6 (1998) 250-265.
[110] K. Tanaka, T. Ikeda, H. O. Wang, Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: Quadric stability, H~∞ control theory, and Linear Matrix Inequalities, IEEE Trans on Fuzzy Systems 8 (2000) 1-12.
[111] K. Tanaka, M. Sugeno, Stability analysis and design of fuzzy control systems, Fuzzy Sets and Systems 45(1992) 135-156.
[112] T. Taniguchi, K. Tanaka, H. Ohtake, H .O. Wang, Model construction, rule reduction, and robust compensation for generalized form of Takagi-Sugeno fuzzy systems, IEEE Trams Fuzzy systems,9(2001) 525-538.
[113] D. Vorobiev, S. Seikkala, Towards the theory of fuzzy differential equations, Fuzzy Sets and Systems 125 (2002) 231-237.
[114] G, Wang and Y. Zhang, The theory of fuzzy stochastic processes,Fuzzy Sets and Systems 51(1992)161-178.
[115] G Wang and Z. Qiao, Convergence of sequences of fuzzy random variables and its application, Fuzzy Sets and Systems 63(1994) 187-199,
[116] H. O. Wang, K. Tanaka, M. F. Griffin, An Approach to fuzzy control of nonlinear systems: stability and design issues, IEEE Trans on Fuzzy Systems 4 (1996) 14-23.
[117] L.X. Wang, Stable adaptive fuzzy controllers with application to inverted pendulum tracking, IEEE Trans. on SMC-Part B, V26, No5, 1996.
[118] Z. Wang, D. W. C. Ho, K. J. Burnham, Robust stability of uncertain stochastic fuzzy systems with time-delays, Technical correspondence. 2002.
[119] H.C. Wu, The central limit theorems for fuzzy random variables, Information Sciences 120 (1999) 239-256.
[120] S. J. Wu, C. T. Lin, Optimal fuzzy controller design in continuous fuzzy system: Global concept approach, IEEE Trans Fuzzy systems 8(2000) 713-729.
[121] S. J. Wu, C .T. Lin, Global optimal fuzzy tracker design based on local concept approach, IEEE Trans Fuzzy systems, 10(2002) 128- 143.
[122] S. Xu, T. Chen, Robust H_∞ control for uncertain stochastic systems with state delay, IEEE Trans Automatic Control 47(2002) 2089-2094.
[123] F. Yang, Z. Wang, Y. S Hung, Robust Kalman filtering for discrete time-varying uncertain systems with multiplicative noises, IEEE Trans Automatic Control 47(2002) 1179-1183.
[124] M. S. Yang, T. S. Lin, Fuzzy least-squares linear regression analysis for fuzzy input-output data, Fuzzy Sets and Systems 126(2002) 389-399.
[125] Y. Yosida, etal., Optimal stopping problems in a stochastic and fuzzy system, J. Math Anal. Appl. 246(2000) 135-149.
[126] Y. Yosida, The valuation of European options in uncertain envionment,
European J. Operational Research 145(2003)221-229.
[127] L.A.Zadeh, Fuzzy logic = computing with words, IEEE Trans. on Fuzzy Systems, 4(1996) 103-110.
[128] P. Zeephongsekul and G. Xia, On fuzzy debugging of software programs, Fuzzy Sets and Systems 83(1996)239 - 247.
[129] Y. Zhang, G. Wang and F. Su, The general theory for response analysis of fuzzy stochastic dynamical systems, Fuzzy Sets and Systems 83(1996)369-405.
[130] C. Zhong and G. Zhou, The equivalence of two definition of fuzzy random variables. Preprints of 2nd IFSA Congress, (1987)59-62.
[131] S. Zhou and G. Feng, Comment on "Optimal Fuzzy Controller Design: Local Concept Approach", IEEE Trans Fuzzy systems, 11(2003) 279-280
[132] Z. Zmeskal, Application of the fuzzy-stochastic methodology to appraising the firm value as a European call option, European Journal of Operational Research, 135 (2001) 303-310
[133] 丁永生，应浩，任立红，邵世煌，解析模糊控制理论：模糊控制系统的结构和稳定性分析，控制与决策，2000，15(2)：29-135．
[134] 冯玉瑚，模糊随机微分方程，中国纺织大学学报，1999，25(1)82-86．
[135] 郭尚来，随机控制，清华大学出版社，1999。
[136] 哈明虎，王光远，连续时间模糊随机系统分析—状态空间模型分析， 哈尔滨建筑大学学报，30(5)，1992：1-10．
[137] 韩崇昭，王月娟，万百五，随机系统理论，西安交通大学出版社，西安，1987。
[138] 胡良剑，吴让泉．模糊随机变量的均方收敛性，中国纺织大学学报， 1998，24(5)：57-60
[139] 雷耀斌，吴让泉．模糊随机系统的卡尔曼滤波，中国纺织大学学报， 1998，24(3)：79-82
[140] 李寿梅，关于Fuzzy随机变量的进一步讨论，河北大学学报，1990，10(4)：8-13．
[141] 廖晓昕，动力系统稳定性理论和应用，北京：国防工业出版社，2000．
[142] 刘晓东，张庆灵，王岩， 基于LMI的T-S模糊系统的H_∞控制，控制与决策，2002，17(6)：924-927．
[143] 欧进萍，吴波，王光远，模糊随机过程与模糊随机微分方程的解法， 哈尔滨建筑工程学院学报，25卷1期(1992)1-10．
[144] 汤兵勇，模糊大系统的自适应协调控制算法，中国控制会议论文集， 1995．
[145] 冯纯伯，田玉平，忻欣，鲁棒控制系统设计，东南大学出版社，1995。
[146] 王光远，乔忠，随机线性规划的单纯形法与模糊随机线性规划的解法，哈尔滨建筑工程学院学报，26卷6期(1993)1-6．
[147] 王立新，模糊系统：挑战与机遇并存．十年研究之感悟，自动化学报， 2001，27(4)：585-590．
[148] 吴从忻，马明，方锦暄．模糊分析学的结构理论．贵州科技出版社， 1994
[149] 吴从忻，马明．模糊分析学基础．国防工业出版社，1991
[150] 吴让泉，胡良剑．二阶模糊随机过程的均方收敛性及其应用．数理 统计与应用概率，1998，13(3)：175-182
[151] 谢立，何星，张卫东，许晓鸣，非线性不确定随机多重时滞系统的
鲁棒H_∞控制，控制与决策，2001，16(增刊)：779-786．
[152] 应浩，关于模糊控制理论与应用的若干问题，自动化学报，2001， 27(4)：591-592．
[153] 俞立，鲁棒控制——线性矩阵不等式方法，清华大学出版社，2002。
[154] 张炳根，赵玉芝．科学与工程中的随机微分方程．海洋出版社，1980。
[155] 张继国，张文修，模糊随机变量及其概率分布，模糊系统与数学， 1996，lO(4)：76-82．
[156] 张世英，王东，基金投资行为及其监管的模糊随机理论研究，管理科学学报，2000，3(1)：58-65． _
[157] 张文修，刘道远，随机F集及其性质，模糊系统与数学，1990,：4(2)1-9．
[158] 张跃，王光远．模糊随机动力系统理论．科学出版社，1993
[159] 周克敏，J．C．Doyle，K．Glover,鲁棒与最优控制，北京：国防工业出版社，2002．
[160] 周智，于朝霞，模糊随机变量的数字特征，模糊系统与数学，1990，4(1)．49-54．