基于T-S模糊模型的复杂非线性大系统的滤波器设计
|
摘要
随着现代科学技术的发展,许多现实生活中的系统比如:电力系统、核反应系统、航天系统、过程控制系统等等,系统的规模越来越大,结构也日趋复杂,同时还具备很强的非线性。解决这类系统问题的两大难点就是系统的大尺度特性和强非线性。大系统理论的提出,将一个高维数的系统从结构上视为多个子系统相互关联耦合而构成,从而可以将大系统的分析与设计建立在相对低维的子系统之上,降低了分析与设计的复杂度;同时针对系统的非线性问题,由于模糊建模的独特优越性,模糊系统理论已逐渐成为分析非线性系统的方法。作为控制的对偶问题,滤波问题对于信号估计、系统输出反馈控制方面有很大的工程指导意义。本文就通过利用大系统和模糊系统的理论相结合分析复杂非线性大系统的滤波器设计问题。论文的主要工作如下:
本文的研究主要基于三类的模糊大系统:连续时间的模糊大系统、离散时间的模糊大系统、时延时变的模糊大系统。
首先,针对一系列连续时间的模糊大系统,基于Lyapunov理论,同时采用分散的设计方法,分别分析了系统的H_∞, H_ 2,混合H_∞H_2滤波问题。将滤波器设计的充分条件转化为一系列的线性不等式。从而得到了连续系统的模糊滤波器设计。
其次,针对离散时间的模糊大系统,同样采用分散的设计方法和Lyapunov理论,设计了系统的H_∞, H_ 2滤波器,同时采用带有线性矩阵不等式约束的凸优化方法设计混合H_∞H_2滤波器,在保证预定H_∞性能的同时使得H_ 2的性能指标最小。
最后,针对时变时延的离散模糊大系统,基于赖于时延的分段二次Lyapunov泛函(DDPLKF),采用自由权矩阵方法和分散的设计方法,分析了大系统的H_∞滤波器问题。最后通过一系列的线性矩阵不等式给出系统赖于时延的H_∞滤波器设计,以及不赖于时延的滤波器设计。
Many real-life systems such as: power systems, nuclear reactor systems, space systems, process control systems, etc., have increasingly large in scale and complex in structure. And these systems are nonlinear systems. Two problems of such systems are the large-scale features and nonlinear. The methodologies of large-scale systems provide techniques through the manipulation of system structure in some way to overcome these problems. The large-scale systems are divided into numbers of subsystems which have connection between each other. Considering the nonlinear problems, due to the unique advantages of fuzzy modeling, fuzzy systems theory has gradually become the analysis method of nonlinear systems. As a dual problem of control, the filtering problem has an important significance for signal estimation, output feedback control system and so on. In this paper, by combining large-scale systems theory and fuzzy systems theory, we have studied the filter design problem of complex nonlinear large-scale system. The main work is as follows: our works are based on three kinds of systems: continuous time fuzzy large-scale system, discrete-time fuzzy large-scale system, and discrete-time fuzzy large-scale system with time-varying delay.
1. We present the filter design for continuous time fuzzy large-scale system. Based on Lyapunov theory, we have analyze the H_∞, H_2, mixed H∞H_2filtering problem respectively with the decentralized approach. It will be shown that the resulting error system is asymptotically stable with guaranteed H_∞and generalized H_2 performance by solving a set of linear matrix inequalities.
2. Based on Lyapunov theory and decentralized approach, we concerned with decentralized H_∞, H_2、H∞H_2filter design for discrete time fuzzy large-scale systems. The main objective is to design stable filters that minimize a guaranteed cost index and achieve a prescribed H_∞performance. The sufficient conditions are established by solving a convex optimization problem with linear matrix inequalities constraint.
3. We have studied the problem of delay-dependent H_∞filter design for a class of discrete-time nonlinear interconnected system with time-varying delays. Based on the delay-dependent piecewise Lyapunov-Krasovskii functional and with an improved free weighting matrix technique, the delay-dependent stability and a pre-scribed H_∞performance are guaranteed for overall filtering error system. A sufficient condition for the existence of such a filter is established by using linear matrix inequalities that are numerically feasible.
本文的研究主要基于三类的模糊大系统:连续时间的模糊大系统、离散时间的模糊大系统、时延时变的模糊大系统。
首先,针对一系列连续时间的模糊大系统,基于Lyapunov理论,同时采用分散的设计方法,分别分析了系统的H_∞, H_ 2,混合H_∞H_2滤波问题。将滤波器设计的充分条件转化为一系列的线性不等式。从而得到了连续系统的模糊滤波器设计。
其次,针对离散时间的模糊大系统,同样采用分散的设计方法和Lyapunov理论,设计了系统的H_∞, H_ 2滤波器,同时采用带有线性矩阵不等式约束的凸优化方法设计混合H_∞H_2滤波器,在保证预定H_∞性能的同时使得H_ 2的性能指标最小。
最后,针对时变时延的离散模糊大系统,基于赖于时延的分段二次Lyapunov泛函(DDPLKF),采用自由权矩阵方法和分散的设计方法,分析了大系统的H_∞滤波器问题。最后通过一系列的线性矩阵不等式给出系统赖于时延的H_∞滤波器设计,以及不赖于时延的滤波器设计。
Many real-life systems such as: power systems, nuclear reactor systems, space systems, process control systems, etc., have increasingly large in scale and complex in structure. And these systems are nonlinear systems. Two problems of such systems are the large-scale features and nonlinear. The methodologies of large-scale systems provide techniques through the manipulation of system structure in some way to overcome these problems. The large-scale systems are divided into numbers of subsystems which have connection between each other. Considering the nonlinear problems, due to the unique advantages of fuzzy modeling, fuzzy systems theory has gradually become the analysis method of nonlinear systems. As a dual problem of control, the filtering problem has an important significance for signal estimation, output feedback control system and so on. In this paper, by combining large-scale systems theory and fuzzy systems theory, we have studied the filter design problem of complex nonlinear large-scale system. The main work is as follows: our works are based on three kinds of systems: continuous time fuzzy large-scale system, discrete-time fuzzy large-scale system, and discrete-time fuzzy large-scale system with time-varying delay.
1. We present the filter design for continuous time fuzzy large-scale system. Based on Lyapunov theory, we have analyze the H_∞, H_2, mixed H∞H_2filtering problem respectively with the decentralized approach. It will be shown that the resulting error system is asymptotically stable with guaranteed H_∞and generalized H_2 performance by solving a set of linear matrix inequalities.
2. Based on Lyapunov theory and decentralized approach, we concerned with decentralized H_∞, H_2、H∞H_2filter design for discrete time fuzzy large-scale systems. The main objective is to design stable filters that minimize a guaranteed cost index and achieve a prescribed H_∞performance. The sufficient conditions are established by solving a convex optimization problem with linear matrix inequalities constraint.
3. We have studied the problem of delay-dependent H_∞filter design for a class of discrete-time nonlinear interconnected system with time-varying delays. Based on the delay-dependent piecewise Lyapunov-Krasovskii functional and with an improved free weighting matrix technique, the delay-dependent stability and a pre-scribed H_∞performance are guaranteed for overall filtering error system. A sufficient condition for the existence of such a filter is established by using linear matrix inequalities that are numerically feasible.
引文
[1] D. D. Siljak. Large-scale dynamic systems: stability and structure. Elsevier North-Hollad: New York, 1978.
[2]涂序彦.大系统控制论.国防工业出版社, 1994.
[3] T. N. Lee, U. L. Radovic. General decentralized stabilization of large-scale system linear continuous and discrete time-delay systems. International Journal of Control, 1987, 46(6): 2127-2140.
[4] W. J. Wang, L. G. Mau. Stabilization and estimation for perturbed discrete time-delay large-scale systems. IEEE Transactions on Automatic Control, 1997, 42(9): 1277-1282.
[5] UA Khan, JMF Moura. Distributing the Kalman filter for large-scale systems. IEEE Transactions on Signal Processing, 2008, 56(10): 4919-4935.
[6] P. Shi, Y. Y. Wang, L. H. Xie. Robust filtering for inter-connected uncertain systems under sampled measurements. Journal of Dynamic Systems, Measurement, and Control-Transactions of The ASME, 1997, 119(2): 337-340.
[7] K. K. Shyu, W. J. Liu, K. C. Hsu. Decentralised variable structure control of uncertain large-scale systems containing a dead-zone. IEE-Proceedings Control Theory and Applications, 2003, 150(5): 1350-2379.
[8] E. H. Mamdani. Application of fuzzy logic to approximate reasoning using linguistic synthesis. IEEE Transactions on Computers, 1977, 26(12): 1182-1191.
[9] Elie Sanchez. Resolution of composite fuzzy relation equations. Information and Control, 1976, 30(1): 38-48.
[10] S. A. Orlovsky. Decision-making with a fuzzy preference relation. Fuzzy Sets and Systems, 1978, 1(3),: 155-167.
[11] Huibert Kwakernaak. Fuzzy random variables—1. definitions and theorems. Information Sciences, 1978, 15(1): 1-29.
[12] H. J. Zimmermann. Fuzzy programming and linear programming with several objective functions*1. Fuzzy Sets and Systems, 1978, 1(1): 45-55.
[13] Kazuo Tanaka, Hua O. Wang. Fuzzy control systems design and analysis: a linear matrix inequality approach. John Wiley & Sons: New York, 2001.
[14] G. Feng, A Survey on Analysis and Design of Model-Based Fuzzy Control Systems. IEEE Transactions on Fuzzy Systems, 2006, 14(5): 676-697.
[15] T. Takagi, M. Sugeno. Fuzzy Identification of Systems and Its Applications: Modeling and Control. IEEE Transactions on System, Man and Cybernet-ics, 1985, 15(1): 116-132.
[16] K. Tanaka, M. Sano. Fuzzy Stability Criterion of a Class of Nonlinear Systems. Information Science, 1993, 70(1-2): 3-26.
[17] S. G. Cao, N. W. Rees, G. Feng. Stability Analysis and Design for a Class of Continuous-Time Fuzzy Control Systems. International Journal of Control, 1996, 64: 1069-1087.
[18] K. Tanaka, T. Ikeda, H. O. Wang. Fuzzy Regulators and Fuzzy Observers: Relaxed Stability Conditions and LMI-Based Designs. IEEE Transactions on Fuzzy Systems, 1998, 6: 250-265.
[19] H. J. Lee, J. B. Park, G. Chen. Robust Fuzzy Control of Nonlinear Systems with Parametric Uncertainties. IEEE Transactions on Fuzzy Systems, 2001, 9(2): 369-379.
[20] Y. Y. Cao, P. M. Frank, Robust H∞Disturbance Attenuation for a Class of Uncertain Discrete-Time Fuzzy Systems. IEEE Transactions on Fuzzy Systems, 2000, 8: 200-211.
[21] E. Kim, D. Kim. Stability Analysis and Synthesis for an Affine Fuzzy Systems via LMI and LMI: Discrete Case. IEEE Transactions on System, Man and Cybernet-ics part B, 2001, 31:132-140.
[22] X. P. Guan, C. L. Chen. Delay-Dependent Guaranteed Cost Control for T-S Fuzzy Systems With Time Delays. IEEE Transactions on Fuzzy Systems, 2004, 12: 236-249.
[23] H. G. Zhang, Y. C. Wang, D. R. Liu, Delay-dependent guaranteed cost control for uncertain Stochastic fuzzy systems with multiple tire delays. IEEE Transactions on System, Man and Cybernet-ics part B, 2008, 38(1): 126-140.
[24] C. Lin. Design of observer-based H-infinity control for fuzzy time-delay systems, IEEE Transactions on Fuzzy Systems, 2008, 16(2):534-543.
[25] C. Lin, Q. G. Wang, T. H. Lee, et al., Fuzzy weighting-dependent approach to H-infinity filter design for time-delay fuzzy systems. IEEE Transactions on Signal Processing, 2007, 55(6): 2746-2751.
[26] T. J. Zhang, G. Feng, J. H. Lu. Fuzzy Constrained Min-max Model Predictive Control Based on Piecewise Lyapunov Functions. IEEE Transactions on Fuzzy Systems, 2007, 15(4): 686-698.
[27] H. B. Zhang, C. Y. Dang. Piecewise H∞Controller Design of Uncertain Discrete-Time Fuzzy Systems With Time Delays, IEEE Transactions on Fuzzy Systems, 2008, 16(6): 1649-1655.
[28] M. Johansson, A. Rantzer, and K. Arzen. Piecewise quadratic stability of fuzzy system, IEEETransactions on Fuzzy Systems, 1999, 7(6): 713-722.
[29] G. Feng. Controller Synthesis of Fuzzy Dynamic Systems Based on piecewise Lyapunov Functions, IEEE Transactions on Fuzzy Systems, 2003, 11(5): 605-612.
[30] F. H. Hsiao, I. D. Hwang. Stability analysis of fuzzy large-scale systems. IEEE Transactions on systems,Man and Cybernet-ics part B, 2002, 32(1): 122-126.
[31] W. J. Wang. Stability and stabilization of fuzzy large-scale systems. IEEE Transactions on Fuzzy Systems, 2004, 12(3): 309-314.
[32] C. S. Tseng. A novel approach on H∞decentralized fuzzy observer-based fuzzy control design for nonlinear interconnected systems. IEEE Transactions on Fuzzy Systems, 2008, 16(5): 1337-1350.
[33] Z. Hu. Decentralized stabilization of large-scale interconnection systems with delays. IEEE Transactions on Automatic control, 1994, 39(1): 180-182.
[34] S. J. Liu, J. F. Zhang, Z. P. Jiang. Decentralized adaptive output-feedback stabilization for large-scale stochastic nonlinear. Automatic, 2007, 43(2): 238-251.
[35] Hongbin Zhang, Xiaofeng Liao, Chunguang Li, Stability analysis and H∞controller design for large-scale fuzzy systems based on piecewise Lyapunov functions. IEEE Transactions on System, Man and Cybernet-ics part B, 2006, 36(3): 685-698.
[36] Hongbin Zhang, Gang Feng. Stability analysis and H∞controller design of discrete-time fuzzy large-scale systems based on piecewise Lyapunov functions, IEEE Transactions on systems,Man and Cybernet-ics part B, 2008, 38(5): 1390-1401.
[37] F. W. Yang. Robust H 2 filtering for a class of systems with stochastic nonlinearities. IEEE Transactions on Circuits and Systems, 2006, 53(3): 235-239.
[38] F. Zheng. A robust H 2 filtering approach and its application to equalizer for communication systems. IEEE Transactions on signal processing, 2005, 53(8): 2735-3747.
[39] H. B. Zhang, Zhong Hua, et al. Decentralized fuzzy H∞Filtering for large-scale systems. International Conference on Communications, Circuits and Systems Proceedings, 2009, vol.1: 573-576.
[40] H. Gao, Y. Zhao, J. Lam, et al. H∞fuzzy filtering of nonlinear systems with intermittent measurements. IEEE Transactions on Fuzzy Systems, 2009, vol.17: 291-300.
[41] H. B. Zhang, C. Y. dang, C. G. Li. Decentralized H∞filter design for discrete-time interconnected fuzzy systems. IEEE Transactions on Fuzzy Systems, 2009, 17(6): 1428-1440.
[42] Y. C. Lin, J. C. Lo. Robust mixed H 2/ H∞filtering for time-delay systems. IEEE Transactionson signal processing, 2006, 54(8): 2897-2909.
[43]廖晓昕.稳定性的理论、方法和应用.武汉:华中科技大学出版社,1994.
[44]俞立.鲁棒控制-线性矩阵不等式.北京:清华大学出版社,2002.
[45]张友刚.基于LMI的一类关联模糊大系统的稳定性分析及分散控制器设计[学位论文].西南交通大学. 2003.
[46] J. T. Spooner, K. M. Passino. Decentralized adaptive control of nonlinear systems using radial basis neural networks. IEEE Transactions on Automatic Control, 1999, 44(11): 2050-2057.
[47] G. Feng, M. Chen, D. Sun, et al. Approaches to robust filtering design of discrete time fuzzy dynamic systems. IEEE Transactions on Fuzzy Systems, 2008, 16(2): 331-340.
[48] J. B. Qiu, G. Feng. A new design of delay-dependent robust H∞filtering for discrete-time T-S fuzzy systems with time-varying delay. IEEE Transactions on Fuzzy Systems, 2009, 17(5): 1044-1058.
[49] M. Chen, G. Feng, H. B. Ma, et al. Delay-dependent H∞filter design for discrete-time fuzzy systems with time-varying delays. IEEE Transactions on Fuzzy Systems, 2009, 17(3): 604-616.
[50] H. B. Zhang, C. Y. Dang, C. G. Li. Decentralized H∞filter design for discrete-time interconnected fuzzy systems. IEEE Transactions on Fuzzy Systems, 2009, 17(6): 1428-1440.
[51] H. B. Zhang, Y. Y. Shen, G. Feng. Delay-dependent stability and H∞control for a class of fuzzy descriptor systems with time-delay. Fuzzy Sets and Systems, 2009, 160(12): 1689-1707.
[52] H. B. Zhang, C. Y. Dang, J. Zhang. Decentralized fuzzy H∞filtering for nonlinear interconnected systems with multiple delays. IEEE Transactions on Systems, Man, and Cybernetics-Part B; 2010, 40(4): 1197-1203.
[2]涂序彦.大系统控制论.国防工业出版社, 1994.
[3] T. N. Lee, U. L. Radovic. General decentralized stabilization of large-scale system linear continuous and discrete time-delay systems. International Journal of Control, 1987, 46(6): 2127-2140.
[4] W. J. Wang, L. G. Mau. Stabilization and estimation for perturbed discrete time-delay large-scale systems. IEEE Transactions on Automatic Control, 1997, 42(9): 1277-1282.
[5] UA Khan, JMF Moura. Distributing the Kalman filter for large-scale systems. IEEE Transactions on Signal Processing, 2008, 56(10): 4919-4935.
[6] P. Shi, Y. Y. Wang, L. H. Xie. Robust filtering for inter-connected uncertain systems under sampled measurements. Journal of Dynamic Systems, Measurement, and Control-Transactions of The ASME, 1997, 119(2): 337-340.
[7] K. K. Shyu, W. J. Liu, K. C. Hsu. Decentralised variable structure control of uncertain large-scale systems containing a dead-zone. IEE-Proceedings Control Theory and Applications, 2003, 150(5): 1350-2379.
[8] E. H. Mamdani. Application of fuzzy logic to approximate reasoning using linguistic synthesis. IEEE Transactions on Computers, 1977, 26(12): 1182-1191.
[9] Elie Sanchez. Resolution of composite fuzzy relation equations. Information and Control, 1976, 30(1): 38-48.
[10] S. A. Orlovsky. Decision-making with a fuzzy preference relation. Fuzzy Sets and Systems, 1978, 1(3),: 155-167.
[11] Huibert Kwakernaak. Fuzzy random variables—1. definitions and theorems. Information Sciences, 1978, 15(1): 1-29.
[12] H. J. Zimmermann. Fuzzy programming and linear programming with several objective functions*1. Fuzzy Sets and Systems, 1978, 1(1): 45-55.
[13] Kazuo Tanaka, Hua O. Wang. Fuzzy control systems design and analysis: a linear matrix inequality approach. John Wiley & Sons: New York, 2001.
[14] G. Feng, A Survey on Analysis and Design of Model-Based Fuzzy Control Systems. IEEE Transactions on Fuzzy Systems, 2006, 14(5): 676-697.
[15] T. Takagi, M. Sugeno. Fuzzy Identification of Systems and Its Applications: Modeling and Control. IEEE Transactions on System, Man and Cybernet-ics, 1985, 15(1): 116-132.
[16] K. Tanaka, M. Sano. Fuzzy Stability Criterion of a Class of Nonlinear Systems. Information Science, 1993, 70(1-2): 3-26.
[17] S. G. Cao, N. W. Rees, G. Feng. Stability Analysis and Design for a Class of Continuous-Time Fuzzy Control Systems. International Journal of Control, 1996, 64: 1069-1087.
[18] K. Tanaka, T. Ikeda, H. O. Wang. Fuzzy Regulators and Fuzzy Observers: Relaxed Stability Conditions and LMI-Based Designs. IEEE Transactions on Fuzzy Systems, 1998, 6: 250-265.
[19] H. J. Lee, J. B. Park, G. Chen. Robust Fuzzy Control of Nonlinear Systems with Parametric Uncertainties. IEEE Transactions on Fuzzy Systems, 2001, 9(2): 369-379.
[20] Y. Y. Cao, P. M. Frank, Robust H∞Disturbance Attenuation for a Class of Uncertain Discrete-Time Fuzzy Systems. IEEE Transactions on Fuzzy Systems, 2000, 8: 200-211.
[21] E. Kim, D. Kim. Stability Analysis and Synthesis for an Affine Fuzzy Systems via LMI and LMI: Discrete Case. IEEE Transactions on System, Man and Cybernet-ics part B, 2001, 31:132-140.
[22] X. P. Guan, C. L. Chen. Delay-Dependent Guaranteed Cost Control for T-S Fuzzy Systems With Time Delays. IEEE Transactions on Fuzzy Systems, 2004, 12: 236-249.
[23] H. G. Zhang, Y. C. Wang, D. R. Liu, Delay-dependent guaranteed cost control for uncertain Stochastic fuzzy systems with multiple tire delays. IEEE Transactions on System, Man and Cybernet-ics part B, 2008, 38(1): 126-140.
[24] C. Lin. Design of observer-based H-infinity control for fuzzy time-delay systems, IEEE Transactions on Fuzzy Systems, 2008, 16(2):534-543.
[25] C. Lin, Q. G. Wang, T. H. Lee, et al., Fuzzy weighting-dependent approach to H-infinity filter design for time-delay fuzzy systems. IEEE Transactions on Signal Processing, 2007, 55(6): 2746-2751.
[26] T. J. Zhang, G. Feng, J. H. Lu. Fuzzy Constrained Min-max Model Predictive Control Based on Piecewise Lyapunov Functions. IEEE Transactions on Fuzzy Systems, 2007, 15(4): 686-698.
[27] H. B. Zhang, C. Y. Dang. Piecewise H∞Controller Design of Uncertain Discrete-Time Fuzzy Systems With Time Delays, IEEE Transactions on Fuzzy Systems, 2008, 16(6): 1649-1655.
[28] M. Johansson, A. Rantzer, and K. Arzen. Piecewise quadratic stability of fuzzy system, IEEETransactions on Fuzzy Systems, 1999, 7(6): 713-722.
[29] G. Feng. Controller Synthesis of Fuzzy Dynamic Systems Based on piecewise Lyapunov Functions, IEEE Transactions on Fuzzy Systems, 2003, 11(5): 605-612.
[30] F. H. Hsiao, I. D. Hwang. Stability analysis of fuzzy large-scale systems. IEEE Transactions on systems,Man and Cybernet-ics part B, 2002, 32(1): 122-126.
[31] W. J. Wang. Stability and stabilization of fuzzy large-scale systems. IEEE Transactions on Fuzzy Systems, 2004, 12(3): 309-314.
[32] C. S. Tseng. A novel approach on H∞decentralized fuzzy observer-based fuzzy control design for nonlinear interconnected systems. IEEE Transactions on Fuzzy Systems, 2008, 16(5): 1337-1350.
[33] Z. Hu. Decentralized stabilization of large-scale interconnection systems with delays. IEEE Transactions on Automatic control, 1994, 39(1): 180-182.
[34] S. J. Liu, J. F. Zhang, Z. P. Jiang. Decentralized adaptive output-feedback stabilization for large-scale stochastic nonlinear. Automatic, 2007, 43(2): 238-251.
[35] Hongbin Zhang, Xiaofeng Liao, Chunguang Li, Stability analysis and H∞controller design for large-scale fuzzy systems based on piecewise Lyapunov functions. IEEE Transactions on System, Man and Cybernet-ics part B, 2006, 36(3): 685-698.
[36] Hongbin Zhang, Gang Feng. Stability analysis and H∞controller design of discrete-time fuzzy large-scale systems based on piecewise Lyapunov functions, IEEE Transactions on systems,Man and Cybernet-ics part B, 2008, 38(5): 1390-1401.
[37] F. W. Yang. Robust H 2 filtering for a class of systems with stochastic nonlinearities. IEEE Transactions on Circuits and Systems, 2006, 53(3): 235-239.
[38] F. Zheng. A robust H 2 filtering approach and its application to equalizer for communication systems. IEEE Transactions on signal processing, 2005, 53(8): 2735-3747.
[39] H. B. Zhang, Zhong Hua, et al. Decentralized fuzzy H∞Filtering for large-scale systems. International Conference on Communications, Circuits and Systems Proceedings, 2009, vol.1: 573-576.
[40] H. Gao, Y. Zhao, J. Lam, et al. H∞fuzzy filtering of nonlinear systems with intermittent measurements. IEEE Transactions on Fuzzy Systems, 2009, vol.17: 291-300.
[41] H. B. Zhang, C. Y. dang, C. G. Li. Decentralized H∞filter design for discrete-time interconnected fuzzy systems. IEEE Transactions on Fuzzy Systems, 2009, 17(6): 1428-1440.
[42] Y. C. Lin, J. C. Lo. Robust mixed H 2/ H∞filtering for time-delay systems. IEEE Transactionson signal processing, 2006, 54(8): 2897-2909.
[43]廖晓昕.稳定性的理论、方法和应用.武汉:华中科技大学出版社,1994.
[44]俞立.鲁棒控制-线性矩阵不等式.北京:清华大学出版社,2002.
[45]张友刚.基于LMI的一类关联模糊大系统的稳定性分析及分散控制器设计[学位论文].西南交通大学. 2003.
[46] J. T. Spooner, K. M. Passino. Decentralized adaptive control of nonlinear systems using radial basis neural networks. IEEE Transactions on Automatic Control, 1999, 44(11): 2050-2057.
[47] G. Feng, M. Chen, D. Sun, et al. Approaches to robust filtering design of discrete time fuzzy dynamic systems. IEEE Transactions on Fuzzy Systems, 2008, 16(2): 331-340.
[48] J. B. Qiu, G. Feng. A new design of delay-dependent robust H∞filtering for discrete-time T-S fuzzy systems with time-varying delay. IEEE Transactions on Fuzzy Systems, 2009, 17(5): 1044-1058.
[49] M. Chen, G. Feng, H. B. Ma, et al. Delay-dependent H∞filter design for discrete-time fuzzy systems with time-varying delays. IEEE Transactions on Fuzzy Systems, 2009, 17(3): 604-616.
[50] H. B. Zhang, C. Y. Dang, C. G. Li. Decentralized H∞filter design for discrete-time interconnected fuzzy systems. IEEE Transactions on Fuzzy Systems, 2009, 17(6): 1428-1440.
[51] H. B. Zhang, Y. Y. Shen, G. Feng. Delay-dependent stability and H∞control for a class of fuzzy descriptor systems with time-delay. Fuzzy Sets and Systems, 2009, 160(12): 1689-1707.
[52] H. B. Zhang, C. Y. Dang, J. Zhang. Decentralized fuzzy H∞filtering for nonlinear interconnected systems with multiple delays. IEEE Transactions on Systems, Man, and Cybernetics-Part B; 2010, 40(4): 1197-1203.