两类连续系统在不同采样方式下的采样控制
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摘要
近年来,由于数字测量技术和智能设备的快速发展,许多控制系统都是由连续时间对象和离散的控制律(一般由数字计算机来实现)所构成的采样控制系统.在这类系统中,采用不同的采样策略,会直接影响系统的稳定性和性能.所以,对采样控制系统的采样控制的研究是一个非常有意义的热点研究课题.另外,工业中的许多被控对象都具有非线性的特性,已经证明Takagi-Sugeno (T-S)模糊系统是逼近非线性系统的万能逼近器,在一个凸的紧集内,它能够以任意的精度来逼近任何的非线性函数.因此,基于T-S模糊模型表示的非线性系统的随机采样控制的研究具有重要的理论价值和实际意义.
本文的主要研究工作如下：
在第一章中,介绍了本文研究内容的理论和实际意义,以及国内外研究现状.
在第二章中,研究了一类非线性连续系统的随机采样控制问题.为了叙述简便,我们仅考虑两个不同的采样周期,采样的概率是给定的常数且满足伯努利分布,得到的结论也能进一步推广到具有多个随机采样周期的情形.利用输入时滞方法,将具有随机采样率的一类非线性系统建模为在状态中带有时延的连续T-S模糊模型.基于Lyapunov稳定性理论,给出了一类非线性连续系统随机采样控制的均方渐近稳定性条件,并以线性矩阵不等式的形式给出了控制器设计方法.最后,给出了个数值例子来说明所给方法的有效性.
在第三章中,研究了在状态分类多率采样下的线性系统的指数镇定问题.由于对状态的不同分量采样时所用的传感器不同和采样周期也可能不同,为使控制器利用实时的采样信息,我们将状态的分量重新进行分类,然后对同一分向量中的分量利用相同的采样周期进行采样,我们称这种采样策略为状态分类多率采样(CSMS).利用输入时滞方法,将具有CSMS的采样控制系统建模为具有时延的切换系统.基于切换系统方法和Lyapunov稳定性理论,给出这类系统指数稳定的充分条件以及通过求解一组LMI给出相应的切换-采样控制器的设计方法.最后,为了说明所给方法的优点,与状态在单率采样下的采样控制系统的控制器设计方法进行了比较,通过旋转底座倒立摆和自主车泊车的控制例子说明所给方法的有效性.
在第四章中,对本文的研究结论做了总结,并对后续工作进行了展望.
Recently, with the rapid development of digital measurement technology and intelligent instrument, many control systems consist of continuous-time plants and discrete-time controllers (which can be implemented by digital computer, etc.), that is sampled-data control systems. In such systems, adopting different sampling schemes may affect the stability and performance of the systems directly. So it is a significant issue to investigate the sampled-data control for sampled-data control systems. On the other hand, many plants in industry have severe nonlinear characteristics. T-S fuzzy models are shown to be universal function approximators in the sense that they are able to approximate any smooth nonlinear function to any degree of accuracy in any convex compact region. Hence, it is important to investigate the stochastic sampled-data control for nonlinear systems based on T-S fuzzy models both in theory and practice.
The main results in the dissertation are as follows.
In chapter 1, the significance of this thesis is introduced in both theory and application. And the research situation at home and abroad is recalled.
In chapter 2, the problem of stochastic sampled-data control for a class of nonlinear continuous-time systems is investigated. For the sake of presentation simplicity, only two different sampling periods are considered whose occurrence probabilities are given constants and satisfy Bernoulli distribution, which can be further extended to the case with multiple stochastic sampling periods. By using the input delay approach and the T-S fuzzy system method, a class of nonlinear continuous- time systems with stochastic sampling is transformed into a continuous-time T-S fuzzy system with time-varying delays and the stochastic parameters. Based on Lyapunov stability theory, a mean square asymptotic stability condition for the closed-loop T-S fuzzy system is proposed. Furthermore, the controller design method is given in terms of LMI. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.
In chapter 3, the thesis investigates the exponential stabilization problem of linear systems under different sampling period of state sub-vectors. Since the sensors used for sampling different state variables are different and their sampling periods may be different, the state variables are reclassified in order that the controller uses the real-time sampling information and the state variables classified in the identical sub-vector are sampled by one same sampling period. Such sampling scheme is called the classified-states multi-rate sampling (CSMS) in this paper. By the input delay approach, the sampled-data control system with CSMS is modeled as a switched system with time-varying delays. Based on the switched system approach and Lyapunov stability theory, an exponential stability condition for such system is proposed, and the design of the corresponding switched-sampling controller is presented by solving a set of linear matrix inequalities (LMIs). Finally, to demonstrate the merits of the proposed approach, we compare it with the controller design method under single rate sampling of all state variables for the sampled-data control of the rotating base pendulum and closed-loop automobile driving.
In chapter 4, the main results of the thesis are concluded, and some research directions on sampled-data control in future are proposed.
本文的主要研究工作如下：
在第一章中,介绍了本文研究内容的理论和实际意义,以及国内外研究现状.
在第二章中,研究了一类非线性连续系统的随机采样控制问题.为了叙述简便,我们仅考虑两个不同的采样周期,采样的概率是给定的常数且满足伯努利分布,得到的结论也能进一步推广到具有多个随机采样周期的情形.利用输入时滞方法,将具有随机采样率的一类非线性系统建模为在状态中带有时延的连续T-S模糊模型.基于Lyapunov稳定性理论,给出了一类非线性连续系统随机采样控制的均方渐近稳定性条件,并以线性矩阵不等式的形式给出了控制器设计方法.最后,给出了个数值例子来说明所给方法的有效性.
在第三章中,研究了在状态分类多率采样下的线性系统的指数镇定问题.由于对状态的不同分量采样时所用的传感器不同和采样周期也可能不同,为使控制器利用实时的采样信息,我们将状态的分量重新进行分类,然后对同一分向量中的分量利用相同的采样周期进行采样,我们称这种采样策略为状态分类多率采样(CSMS).利用输入时滞方法,将具有CSMS的采样控制系统建模为具有时延的切换系统.基于切换系统方法和Lyapunov稳定性理论,给出这类系统指数稳定的充分条件以及通过求解一组LMI给出相应的切换-采样控制器的设计方法.最后,为了说明所给方法的优点,与状态在单率采样下的采样控制系统的控制器设计方法进行了比较,通过旋转底座倒立摆和自主车泊车的控制例子说明所给方法的有效性.
在第四章中,对本文的研究结论做了总结,并对后续工作进行了展望.
Recently, with the rapid development of digital measurement technology and intelligent instrument, many control systems consist of continuous-time plants and discrete-time controllers (which can be implemented by digital computer, etc.), that is sampled-data control systems. In such systems, adopting different sampling schemes may affect the stability and performance of the systems directly. So it is a significant issue to investigate the sampled-data control for sampled-data control systems. On the other hand, many plants in industry have severe nonlinear characteristics. T-S fuzzy models are shown to be universal function approximators in the sense that they are able to approximate any smooth nonlinear function to any degree of accuracy in any convex compact region. Hence, it is important to investigate the stochastic sampled-data control for nonlinear systems based on T-S fuzzy models both in theory and practice.
The main results in the dissertation are as follows.
In chapter 1, the significance of this thesis is introduced in both theory and application. And the research situation at home and abroad is recalled.
In chapter 2, the problem of stochastic sampled-data control for a class of nonlinear continuous-time systems is investigated. For the sake of presentation simplicity, only two different sampling periods are considered whose occurrence probabilities are given constants and satisfy Bernoulli distribution, which can be further extended to the case with multiple stochastic sampling periods. By using the input delay approach and the T-S fuzzy system method, a class of nonlinear continuous- time systems with stochastic sampling is transformed into a continuous-time T-S fuzzy system with time-varying delays and the stochastic parameters. Based on Lyapunov stability theory, a mean square asymptotic stability condition for the closed-loop T-S fuzzy system is proposed. Furthermore, the controller design method is given in terms of LMI. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.
In chapter 3, the thesis investigates the exponential stabilization problem of linear systems under different sampling period of state sub-vectors. Since the sensors used for sampling different state variables are different and their sampling periods may be different, the state variables are reclassified in order that the controller uses the real-time sampling information and the state variables classified in the identical sub-vector are sampled by one same sampling period. Such sampling scheme is called the classified-states multi-rate sampling (CSMS) in this paper. By the input delay approach, the sampled-data control system with CSMS is modeled as a switched system with time-varying delays. Based on the switched system approach and Lyapunov stability theory, an exponential stability condition for such system is proposed, and the design of the corresponding switched-sampling controller is presented by solving a set of linear matrix inequalities (LMIs). Finally, to demonstrate the merits of the proposed approach, we compare it with the controller design method under single rate sampling of all state variables for the sampled-data control of the rotating base pendulum and closed-loop automobile driving.
In chapter 4, the main results of the thesis are concluded, and some research directions on sampled-data control in future are proposed.
引文
[1]T. Takagi and M. Sugeno. Fuzzy Identification of Systems and Its Applications to Modeling and Control. IEEE Trans, on Syst., Man, Cybern.,1985,15(1),116-132.
[2]王立新,模糊系统与模糊控制教程.北京,清华大学出版社,2003.
[3]H. O. Wang, K. Tanaka, and M. F. Griffin. An Approach to Fuzzy Control of Nonlinear Systems:Stability and Design Issues. IEEE Trans, on Fuzzy Syst.,1996, 4(1),14-23.
[4]K. Tanaka, T. Ikeda, H. O. Wang. Fuzzy Regulators and Fuzzy Observers:Relaxed Stability Conditions and LMI-based Designs. IEEE Trans on Fuzzy Syst.,1998,6(2), 250-65.
[5]K. Tanaka and H. O. Wang. Fuzzy Control Systems Design and Analysis:A Linear Matrix Inequality Approach. Wiley, New York, America,2001.
[6]T. Chen and B. Francis, Optimal Sampled-Data Control Systems. London: Springer-Verlag,1995.
[7]D. Nesic and A. R. Teel. Sampled-data Control of Nonlinear Systems:An Overview of Recent Results. Perspectives Robust Control,2001,268,221-239.
[8]J. Ackerman. Sampled-data Control Systems:Analysis and Synthesis, Robust design. New York, Spinger,1985.
[9]Alessandro Astolfi and Dina Shona Laila. Sampled-Data Control Systems. European control training site gif sur Yvette, France,2005.
[10]H. K. Lam, W. K. Ling. Sampled-data Fuzzy Controller for Continuous Nonlinear Systems, IET Control Theory Appl.,2008,2(1),32-39.
[11]E. Fridman. A Refined Input Delay Approach to Sampled-Data Control, Automatica,2010,46,421-427.
[12]Yasuaki Oishi, Hisaya Fujioka. Stability and Stabilization of Aperiodic Sampled-Data Control Systems Using Robust Linear Matrix Inequalities. Automatica, 2010,46,1327-1333.
[13]Nan Li, Yulian Zhang, Jiawen Hu, Zhenyu Nie. Synchronization for General Complex Dynamical Networks With Sampled-Data. Neurocomputing,2011,74, 805-811.
[14]Jun Yoneyama. Robust Guaranteed Cost Control of Uncertain Fuzzy Systems under Time-Varying Sampling. Applied Soft Computing,2011,11,249-255.
[15]M. Fu, L. Xie. The Sector Bound Approach to Quantized Feedback Control. IEEE Transactions on Automatic Control,2005,50(11),1698-1711.
[16]Huijun Gao, Tongwen Chen. A New Approach to Quantized Feedback Control Systems. Automatica,2008,44,534-542.
[17]Yugang Niu, Tinggang Jia, Xingyu Wang, Fuwen Yang. Output-feedback Control Design for NCSs Subject to Quantization and Dropout. Information Sciences,2009, 179,3804-3813.
[18]Junlin Xiong, Lam, J. Stabilization of Networked Control Systems With a Logic ZOH. IEEE Trans. on Automatic Control,2009,54(2),358-363.
[19]H. Katayama and A. Ichikawa. H∞ Control For Sampled-Data Nonlinear Systems Described by Takagi-Sugeno Fuzzy Systems. Fuzzy Sets Syst,2004,148(3), 431-452.
[20]L. S. Hu, T. Bai, P. Shi, and Z. M. Wu. Sampled-Data Control of Networked Linear Control Systems. Automatica,2007,43(5),903-911.
[21]W. A. Zhang, and Li Yu. Stabilization of Sampled-Data Control Systems With Control Inputs Missing. IEEE Trans, on Automatic Control,2010,55(2),447-452.
[22]L. Xie, Y.J. Liu, H.Z. Yang, F. Ding. Modeling and Identification for Non-Uniformly Periodically Sampled-Data Systems. IET Control Theory and Applications,2010,4(5),784-794.
[23]Huijun Gao, Junli Wu, Peng Shi. Robust Sampled-Data H∞ Control With Stochastic Sampling. Automatica,2009,45(7),1729-1736.
[24]Junli Wu, Xiaoming Chen, Huijun Gao. H∞ Filtering With Stochastic Sampling. Signal Processing,2010,90(4),1131-1145.
[25]Xing Fan, Xinchun Jia, Xiaobo Chi, Xiaokai Wang. Stochastic Sampling Control for A Class of Nonlinear Continuous-time Systems. Proceedings of 2010 Chinese Control and Decision Conference, Xuzhou, China,2010.
[26]Xinchun Jia, Jingmei Zhang, Hongfeng Li, Nanning Zheng. Fuzzy Sampled-Data Control for T-S Continuous-Time Fuzzy Systems. Control Theory & Applications, 2007,24(1),69-74.
[27]Do Wan Kim, Ho Jae Lee, Masayoshi Tomizuka. Fuzzy Stabilization of Nonlinear Systems under Sampled-Data Feedback:An Exact Discrete-Time Model Approach. IEEE Trans. on Fuzzy Syst,2010,18(2),251-260.
[28]Huijun Gao, Tongwen Chen. Stabilization of Nonlinear Systems under Variable Sampling:A Fuzzy Control Approach. IEEE Trans. on Fuzzy Syst,2007,15(5), 972-983.
[29]Dedong Yang, Kaiyuan Cai. Reliable H∞ Nonuniform Sampling Fuzzy Control for Nonlinear Systems with Time Delay. IEEE Trans. on Syst., Man, Cybern. B, Cybern.,2008,38(6),1606-1613.
[30]J. Yoneyama. Robust H∞ Control of Uncertain Fuzzy Systems under Time-Varying Sampling. Fuzzy Sets and Systems,2010,161(6),859-871.
[31]B. Bamieh, J. Pearson, B. Francis, A. Tannenbaum. A Lifting Technique for Linear Periodic Systems. Systems and Control Letters,1991,17(2),79-88.
[32]T. Chen., B. A. Francis. H∞-Optimal Sampled-Data Control:Computation and Design. Automatica,1996,32(2),223-228.
[33]L Hu, H. Shao, Y. Sun. Sampled-Data Control for Time-Delay Uncertain Linear Systems. Control theory and applications,2000,17(3),453-456.
[34]L. Hu, J. Lam, Y. Cao, and H. Shao. A LMI Approach to Robust H2 Sampled-Data Control for Linear Uncertain Systems. IEEE Trans. on Syst., Man, Cybern., B, Cybern.,2003,33(1),149-155.
[35]E. Fridman, A. Seuret, and J. P. Richard. Robust Sampled-Data Stabilization of Linear Systems:An Input Delay Approach. Automatica,2004,40(8),1441-1446.
[36]H. N. Wu. Delay-Dependent Stability and Stabilization for Discrete-Time Fuzzy Systems with Delay:A Fuzzy Lyapunov-Krasovskii Functional Approach. IEEE Trans. Syst. Man Cybern. Part B.2006,36(4),954-962.
[37]G. Feng. Stability Analysis of Discrete-Time Fuzzy Dynamic Systems Based on Piecewise Lyapunov Functions. IEEE Trans. Fuzzy System,2004,12(1),22-28.
[38]H. Wang, K. Tanaka, M. Griffin. Parallel Distributed Compensation of Nonlinear Systems by Takagi and Sugeno's Fuzzy Model. Proceedings of 4th IEEE Int. Conf. Fuzzy Syst.,1995,531-538.
[39]Zidong Wang, Jian'an Fang, Xiaohui Liu. Global Stability of Stochastic High-order Neural Networks with Discrete and Distributed Delays. Chaos, Solitons and Fractals, 2008,36(2),388-396.
[40]S. Boyd, L. El Ghaoui,, E. Feron, V. Balakrishnan. Linear Matrix Inequalities in System and Control Theory. Philadelphia: SIAM,1994.
[41]K. Gu, V. L. Kharitonov, and J. Chen. Stability of Time-Delay systems. Boston: Birkhauser,2003.
[42]Xinchun Jia, Dawei Zhang, Lihong Zheng, and Nanning Zheng. Modeling and Stabilization for A Class of Nonlinear Networked Control Systems:A T-S Fuzzy Approach. Progress in Natural Science,2008,18(8),1031-1037.
[43]K. Gu. An Integral Inequality in the Stability Problem of Time-DelaySystems. Proc. 39th IEEE Conf. on Decision and Control,2805-2810,2000.
[44]Min Wu, Yong He, Jin-Hua She, Guo-Ping Liu. Delay-dependent Criteria for Robust Stability of Time-Varying Delay Systems. Automatica,2004,40(8),1435-1439.
[45]N. J. Ploplys, P. A. Kawaka, and A. G. Alleyne. Closed-loop Control over Wireless Networks. IEEE Control Syst. Mag.,2004,24(3),58-71.
[46]Charles C. Macadam. Application of An Optimal Preview Control for Simulation of Closed-loop Automobile Driving. IEEE Transactions on Systems, Man, And Cybernetics,1981,11(6),393-399.
[47]D. Liberzon. Switching in System and Control. Boston, MA:Birkhauser,2003.
[2]王立新,模糊系统与模糊控制教程.北京,清华大学出版社,2003.
[3]H. O. Wang, K. Tanaka, and M. F. Griffin. An Approach to Fuzzy Control of Nonlinear Systems:Stability and Design Issues. IEEE Trans, on Fuzzy Syst.,1996, 4(1),14-23.
[4]K. Tanaka, T. Ikeda, H. O. Wang. Fuzzy Regulators and Fuzzy Observers:Relaxed Stability Conditions and LMI-based Designs. IEEE Trans on Fuzzy Syst.,1998,6(2), 250-65.
[5]K. Tanaka and H. O. Wang. Fuzzy Control Systems Design and Analysis:A Linear Matrix Inequality Approach. Wiley, New York, America,2001.
[6]T. Chen and B. Francis, Optimal Sampled-Data Control Systems. London: Springer-Verlag,1995.
[7]D. Nesic and A. R. Teel. Sampled-data Control of Nonlinear Systems:An Overview of Recent Results. Perspectives Robust Control,2001,268,221-239.
[8]J. Ackerman. Sampled-data Control Systems:Analysis and Synthesis, Robust design. New York, Spinger,1985.
[9]Alessandro Astolfi and Dina Shona Laila. Sampled-Data Control Systems. European control training site gif sur Yvette, France,2005.
[10]H. K. Lam, W. K. Ling. Sampled-data Fuzzy Controller for Continuous Nonlinear Systems, IET Control Theory Appl.,2008,2(1),32-39.
[11]E. Fridman. A Refined Input Delay Approach to Sampled-Data Control, Automatica,2010,46,421-427.
[12]Yasuaki Oishi, Hisaya Fujioka. Stability and Stabilization of Aperiodic Sampled-Data Control Systems Using Robust Linear Matrix Inequalities. Automatica, 2010,46,1327-1333.
[13]Nan Li, Yulian Zhang, Jiawen Hu, Zhenyu Nie. Synchronization for General Complex Dynamical Networks With Sampled-Data. Neurocomputing,2011,74, 805-811.
[14]Jun Yoneyama. Robust Guaranteed Cost Control of Uncertain Fuzzy Systems under Time-Varying Sampling. Applied Soft Computing,2011,11,249-255.
[15]M. Fu, L. Xie. The Sector Bound Approach to Quantized Feedback Control. IEEE Transactions on Automatic Control,2005,50(11),1698-1711.
[16]Huijun Gao, Tongwen Chen. A New Approach to Quantized Feedback Control Systems. Automatica,2008,44,534-542.
[17]Yugang Niu, Tinggang Jia, Xingyu Wang, Fuwen Yang. Output-feedback Control Design for NCSs Subject to Quantization and Dropout. Information Sciences,2009, 179,3804-3813.
[18]Junlin Xiong, Lam, J. Stabilization of Networked Control Systems With a Logic ZOH. IEEE Trans. on Automatic Control,2009,54(2),358-363.
[19]H. Katayama and A. Ichikawa. H∞ Control For Sampled-Data Nonlinear Systems Described by Takagi-Sugeno Fuzzy Systems. Fuzzy Sets Syst,2004,148(3), 431-452.
[20]L. S. Hu, T. Bai, P. Shi, and Z. M. Wu. Sampled-Data Control of Networked Linear Control Systems. Automatica,2007,43(5),903-911.
[21]W. A. Zhang, and Li Yu. Stabilization of Sampled-Data Control Systems With Control Inputs Missing. IEEE Trans, on Automatic Control,2010,55(2),447-452.
[22]L. Xie, Y.J. Liu, H.Z. Yang, F. Ding. Modeling and Identification for Non-Uniformly Periodically Sampled-Data Systems. IET Control Theory and Applications,2010,4(5),784-794.
[23]Huijun Gao, Junli Wu, Peng Shi. Robust Sampled-Data H∞ Control With Stochastic Sampling. Automatica,2009,45(7),1729-1736.
[24]Junli Wu, Xiaoming Chen, Huijun Gao. H∞ Filtering With Stochastic Sampling. Signal Processing,2010,90(4),1131-1145.
[25]Xing Fan, Xinchun Jia, Xiaobo Chi, Xiaokai Wang. Stochastic Sampling Control for A Class of Nonlinear Continuous-time Systems. Proceedings of 2010 Chinese Control and Decision Conference, Xuzhou, China,2010.
[26]Xinchun Jia, Jingmei Zhang, Hongfeng Li, Nanning Zheng. Fuzzy Sampled-Data Control for T-S Continuous-Time Fuzzy Systems. Control Theory & Applications, 2007,24(1),69-74.
[27]Do Wan Kim, Ho Jae Lee, Masayoshi Tomizuka. Fuzzy Stabilization of Nonlinear Systems under Sampled-Data Feedback:An Exact Discrete-Time Model Approach. IEEE Trans. on Fuzzy Syst,2010,18(2),251-260.
[28]Huijun Gao, Tongwen Chen. Stabilization of Nonlinear Systems under Variable Sampling:A Fuzzy Control Approach. IEEE Trans. on Fuzzy Syst,2007,15(5), 972-983.
[29]Dedong Yang, Kaiyuan Cai. Reliable H∞ Nonuniform Sampling Fuzzy Control for Nonlinear Systems with Time Delay. IEEE Trans. on Syst., Man, Cybern. B, Cybern.,2008,38(6),1606-1613.
[30]J. Yoneyama. Robust H∞ Control of Uncertain Fuzzy Systems under Time-Varying Sampling. Fuzzy Sets and Systems,2010,161(6),859-871.
[31]B. Bamieh, J. Pearson, B. Francis, A. Tannenbaum. A Lifting Technique for Linear Periodic Systems. Systems and Control Letters,1991,17(2),79-88.
[32]T. Chen., B. A. Francis. H∞-Optimal Sampled-Data Control:Computation and Design. Automatica,1996,32(2),223-228.
[33]L Hu, H. Shao, Y. Sun. Sampled-Data Control for Time-Delay Uncertain Linear Systems. Control theory and applications,2000,17(3),453-456.
[34]L. Hu, J. Lam, Y. Cao, and H. Shao. A LMI Approach to Robust H2 Sampled-Data Control for Linear Uncertain Systems. IEEE Trans. on Syst., Man, Cybern., B, Cybern.,2003,33(1),149-155.
[35]E. Fridman, A. Seuret, and J. P. Richard. Robust Sampled-Data Stabilization of Linear Systems:An Input Delay Approach. Automatica,2004,40(8),1441-1446.
[36]H. N. Wu. Delay-Dependent Stability and Stabilization for Discrete-Time Fuzzy Systems with Delay:A Fuzzy Lyapunov-Krasovskii Functional Approach. IEEE Trans. Syst. Man Cybern. Part B.2006,36(4),954-962.
[37]G. Feng. Stability Analysis of Discrete-Time Fuzzy Dynamic Systems Based on Piecewise Lyapunov Functions. IEEE Trans. Fuzzy System,2004,12(1),22-28.
[38]H. Wang, K. Tanaka, M. Griffin. Parallel Distributed Compensation of Nonlinear Systems by Takagi and Sugeno's Fuzzy Model. Proceedings of 4th IEEE Int. Conf. Fuzzy Syst.,1995,531-538.
[39]Zidong Wang, Jian'an Fang, Xiaohui Liu. Global Stability of Stochastic High-order Neural Networks with Discrete and Distributed Delays. Chaos, Solitons and Fractals, 2008,36(2),388-396.
[40]S. Boyd, L. El Ghaoui,, E. Feron, V. Balakrishnan. Linear Matrix Inequalities in System and Control Theory. Philadelphia: SIAM,1994.
[41]K. Gu, V. L. Kharitonov, and J. Chen. Stability of Time-Delay systems. Boston: Birkhauser,2003.
[42]Xinchun Jia, Dawei Zhang, Lihong Zheng, and Nanning Zheng. Modeling and Stabilization for A Class of Nonlinear Networked Control Systems:A T-S Fuzzy Approach. Progress in Natural Science,2008,18(8),1031-1037.
[43]K. Gu. An Integral Inequality in the Stability Problem of Time-DelaySystems. Proc. 39th IEEE Conf. on Decision and Control,2805-2810,2000.
[44]Min Wu, Yong He, Jin-Hua She, Guo-Ping Liu. Delay-dependent Criteria for Robust Stability of Time-Varying Delay Systems. Automatica,2004,40(8),1435-1439.
[45]N. J. Ploplys, P. A. Kawaka, and A. G. Alleyne. Closed-loop Control over Wireless Networks. IEEE Control Syst. Mag.,2004,24(3),58-71.
[46]Charles C. Macadam. Application of An Optimal Preview Control for Simulation of Closed-loop Automobile Driving. IEEE Transactions on Systems, Man, And Cybernetics,1981,11(6),393-399.
[47]D. Liberzon. Switching in System and Control. Boston, MA:Birkhauser,2003.