摘要
T-S模糊广义系统模型能够很好地逼近非线性广义系统,是解决非线性广义系统控制问题的一个有效途径。目前,虽然对T-S模糊广义系统稳定性分析与控制的研究已经取得了一些成果,但是与经典控制理论相比还相差甚远。T-S模糊广义系统的研究尚在初级阶段,还有许多有待解决的问题。本文借鉴线性广义系统理论和现代鲁棒控制理论思想,利用先进的矩阵分析理论和线性矩阵不等式(LMIs)技术,在Lyapunov稳定性理论框架下,研究了一类T-S模糊广义系统的控制问题。主要工作有以下几个方面:
1.研究了一类由T-S模糊广义系统模型描述的连续非线性时滞广义系统的保成本控制问题。首先,以LMIs的形式给出了状态反馈保成本控制器存在的充分条件,并在此基础上利用模糊规则权以及引入新的变量获得一个改进的模糊保成本控制器设计方法,在一定程度上降低了设计的保守性。其次,将具有最小J。值的保成本控制器设计问题转化为一个LMIs约束的凸优化问题来求解。数值算例说明所设计的模糊控制器不仅能保证闭环系统渐近稳定,而且满足最小化的性能指标。最后,研究了基于广义观测器的输出反馈保成本控制问题,以LMIs的形式给出了基于广义观测器的输出反馈保成本控制器存在的充分条件。
2.针对一类由T-S模糊广义系统模型描述的参数不确定的连续非线性时滞广义系统,首先利用Lyapunov稳定性理论和线性矩阵不等式(LMIs)技术研究了系统的二次稳定性,并在此基础上提出鲁棒H∞控制设计方法,以LMIs的形式给出系统二次稳定条件及鲁棒H∞控制器存在的充分条件。其次研究了不确定时滞T-S模糊广义系统的鲁棒保成本控制问题,将具有最小J0值的保成本控制器设计问题转化为一个LMIs约束的凸优化问题来求解。数值算例说明所提出的模糊鲁棒H∞控制器及模糊鲁棒保成本控制器的设计方法的有效性。
3.基于时滞相关准则研究了一类由T-S模糊广义系统模型描述的不确定连续非线性时滞广义系统的鲁棒保成本控制问题,讨论了时滞的大小对稳定性的影响,对于使系统保持渐近稳定所允许的时滞上界max的求取,归结为一个LMI约束的凸优化问题来求解。而相应于允许的时滞上界的保成本性能指标的最小上界则转化为一个寻找次优值的优化问题。仿真结果表明了所提出方法的有效性。
4.基于时滞相关的方法研究了一类由T-S模糊广义系统模型描述的不确定连续非线性时滞广义系统的非脆弱H∞控制问题。首先,针对参数确定的标称系统,提出了一个新的时滞相关H。稳定性判据。其次,考虑系统存在范数约束的参数不确定性时,分别提出了基于两种增益变化形式的非脆弱控制器设计方法。以LMIs的形式给出了满足H∞性能指标的非脆弱控制器存在的充分条件,仿真示例表明所提出方法的有效性。
5.提出了一个多时滞的T-S模糊广义系统模型,并且基于Lyapunov稳定性理论和时滞无关的方法研究了一类由多时滞连续T-S模糊广义系统模型描述的多时滞非线性广义系统的保成本控制问题以及H∞控制问题。以LMIs的形式给出了系统的稳定性条件,以及保成本控制器和H∞控制器存在的充分条件。多时滞T-S模糊广义系统,是对单时滞T-S模糊广义系统的推广,具有更广泛的实际意义。目前在其它文献中还没有研究过。
6.研究了一类由离散T-S模糊时滞广义系统模型描述的离散非线性时滞广义系统的控制问题,首先给出了该类系统的一致正则、因果以及稳定性和容许性的定义,并基于Lyapunov函数方法,对系统的稳定性进行分析,以线性矩阵不等式(LMIs)的形式给出系统一致正则、因果和稳定的充分条件。提出了模糊状态反馈控制器和输出反馈控制器的设计方法。
T-S fuzzy descriptor system model which can approximate a non-linear descriptor system perfectly, is thought to be an effective approach to solve the control problem of non-linear descriptor systems. Currently, although much effort has been made in the exploration of stability analysis and control for the T-S fuzzy descriptor system, the results on this topic are far fewer than those on normal systems. The research on T-S fuzzy descriptor system is still in primary stage. Lots of problems need to be solved. In this paper, by using the advanced matrix theory and the linear matrix inequality (LMIs) technique, we study the problems of stability analysis and control design for a class of T-S fuzzy descriptor systems under the framework of Lyapunov stability theory, which is motivated by the linear descriptor system theory and advanced robust control theory. The main contributions are as follows:
1. The problems of guaranteed cost control of a class of continous time nonlinear descriptor delay systems described by T-S fuzzy descriptor model are studied. First, sufficient conditions of the existence of state feedback guaranteed cost controller are given in terms of LMIs. Then fuzzy rule weights and some new variables are used to obtain an improved guaranteed cost controller design method which is less conservative. And design of guaranteed cost controller with minimized J0 is reduced to a convex optimization problem constrained by LMIs. A numeric example is provided to illustrate the effectiveness of the proposed method. At last, the problem of generalized observer based output feedback guaranteed cost control is discussed. The sufficient conditions of the existence of observer based output feedback guaranteed cost controller are given in terms of LMIs.
2. Aiming at a class of uncertain continous time nonlinear descriptor delay systems described by T-S fuzzy descriptor model, the quadratic stability is studied by using Lyapunov stability theory and LMIs technology. Based on the quadratic stability, the robust H∞control method is proposed. The quadratic stability conditions and the sufficient conditions of the existence of robust H∞controller are given in terms of LMIs. Next, Robust guaranteed cost control for uncertain T-S fuzzy descriptor delay system is discussed. And design of guaranteed cost controller with minimized J0 is reduced to a convex optimization problem constrained by LMIs. numeric examples are provided to illustrate the effectiveness of the proposed methods of robust H∞controller and robust guaranteed cost controller.
3. Based on delay-dependent method, the robust guaranteed cost control of a class of uncertain continous time nonlinear descriptor delay systems described by T-S fuzzy descriptor model is investigated. The relationship between the size of delay and stability is discussed. And the estimation of the upper bound of delayτmax is formulated by a convex optimization problem. The minimized guaranteed cost upper bound corresponding toτmax is reduced to an optimization problem of searching for the suboptimal value. The simulation results indicate the effectiveness of the proposed method.
4. Based on delay-dependent method, the non-fragile H∞control problem of a class of uncertain continous time nonlinear descriptor delay systems described by T-S fuzzy descriptor model is considered. First, a new delay-dependent H∞stability criterion is proposed aiming at the normal system. Then, based on two kinds of gain variations, the design methods of non-fragile controllers satisfying H∞norm bound are provided. The sufficient conditions of the existence of non-fragile H∞controller are given in terms of LMIs. The simulation example indicates the effectiveness of the proposed method.
5. A multiple delay T-S fuzzy descriptor model is proposed. Based on Lyapunov stability theory and delay-independent method, guaranteed cost control and H∞control problems of a class of multiple delay nonlinear descriptor systems described by multiple delay T-S fuzzy descriptor model are studied. The stability conditions and the sufficient conditions of existence of guaranteed cost controller and H∞controller are given in terms of LMIs. I is worth noting that multiple delay T-S fuzzy descriptor system is extension of single delay T-S fuzzy descriptor system. It is of more extensive practical significance, and has not been studied in other literature yet.
6. The control problems of a class of discrete time nonlinear descriptor delay systems described by the discrete time T-S fuzzy descriptor model are considered. First, the definitions of consistent regularity, cause and effect, stability and admissibility are given. Then, The stability of the system is analyzed based on Lyapunov method. The sufficient conditions of the system to be consistent regular, cause and effect and stable are given in terms of LMIs. At last, design methods of state feedback and output feedback controllers are proposed.
引文
1. Zadeh L A. Fuzzy set[J]. Information and Control,1965,8:338-358.
2.王立新.自适应模糊系统与控制——设计与稳定性分析[M],北京:国防工业出版社,1995年.
3.佟绍成,王涛,王艳平等.模糊控制系统的设计及稳定性分析[M],北京:科学出版社,2004年.
4.张化光,何希勤.模糊自适应控制理论及其应用[M],北京:北京航空航天大学出版社,2002.
5. Mamdani E H. Applications of fuzzy algorithms for simple dynamic plant[J]. Proceedings of IEE.1974,121(12):1585-1588.
6. Mamdani, Assilian. Fuzzy sets as a basis for a theory of possibility[J]. Fuzzy Sets and Systems,1978,1(1):3-28.
7. 王立新著,王迎军译.模糊系统与模糊控制教程[M],北京:清华大学出版社,2003.
8.权太范等.模糊控制技术在控制中的应用现状及前景[J],控制与决策,1983,3(1):59-62.
9. Tobi T, et al. The application of fuzzy control to a coke oven gas cooling plant. Fuzzy Sets and Systems,1992,46:373-381.
10. Procyk T J, Mamdani E H. A liguistic self-organizing process controller[J]. Automatica, 1979,15:15-30.
11. Linkens D A, Hasnain S B. Self-organizing fuzzy logic control and application to muscle relaxant anesthesia[J]. IEE Proceedings-D,1991,138(3):274-284.
12. Daleyand S, Gill K F. A design study of a self-organizing fuzzy logic controller[J]. Proc. Instn Mech. Engrs,1986,200:59-69.
13. Sugiyama K. Rule-based self-organizing controller [J]. Fuzzy computing,1988:241-253.
14. Zhang B S, Edmunds J M. Self-organizing fuzzy logic controlle[J]. IEE Proceedings-D, 1992,139(5):460-464.
15. Song J J, Park S. A fuzzy learning controller for chemical process control[J]. Fuzzy Sets and Systems,1993,54:121-133.
16. Linkens D A, Nie J. Constructing rule-bases for multivariable fuzzy control by self-learning, Part I. System structure and learning algorithms [J]. International of Journal Systems Science,1993,24(1):117-127.
17. Kim Y T, Bien Z. Robust self-learning fuzzy controller design for a class of nonlinear MIMO systems[J]. Fuzzy Sets and Systems,2000,111(2):117-135.
18. Layne J R, et al. Fuzzy model reference learning control for cargo ship steering[J].IEEE Transactions on Control Systems,1993,13(5):23-24.
19. He S Z, et al. Design of on-line rule adaptive fuzzy control system[C]. IEEE Conference on Fuzzy System, San Diego, USA,1992:83-91.
20. Raju G V S. Adaptive hierarchical fuzzy controller[J]. IEEE Transactions on Systems, Man, and Cybernetics,1993,23(4):873-980.
21. Gegov A. Multievel intelligent fuzzy control of oversaturated urban tra±c networks[J]. International Journal of Systems Science,1994,25(6):967-978.
22. Han J Y, Viment M M. Two layer multipie-varible fuzzy logic controller[J]. IEEE Transactions on Systems, Man, and Cybernetics,1993,23(1):277-284.
23. Wang L X, Mendel J M. Fuzzy basis functions, universal approximation, and orthogonal least squares learning[J]. IEEE Transactions on Neural Networks,1992,3(5):807-814.
24. Takagi T, Sugeno M. Fuzzy identification of systems and its applications to modeling and control[J]. IEEE Transactions on Systems, Man, and Cybernetics,1985,15(1):116-132.
25. Wang H O, Tanaka K, Griten M F. An approach to fuzzy control of nonlinear systems: stability and design issues[J]. IEEE Transactions on Fuzzy Systems,1996,4(1):14-23.
26. Takagi T, Sugeno M. A robust stabilization problem of fuzzy control systems and its application to backing up control of truck-trailer[J]. Fuzzy Sets and Systems,1994,2(2): 119-133.
27.孙增圻.智能控制理论与技术[M].北京:清华大学出版社,1997.
28.佟绍成,柴天佑.一类多变量非线性动态系统的鲁棒自适应模糊控制[J],自动化学报,2000,26(5):630-636.
29. Cao S G, Rees N W, Feng G. Quadratic stability analysis and design of continuous-time fuzzy control systems[J]. International Journal of Systems Science,1996,27:193-203.
30. Leu Y G, Lee T T, Wang W Y. On-line tuning of fuzzy-neural network for adaptive control of nonlinear dynamical systems[J]. IEEE Transactions on Systems, Man, and Cybernetics,1997,27(7):1034-1043.
31. Kruszewski A, Guerra T M. New approaches for the stabilization of discrete Takagi-Sugeno fuzzy models[C]. IEEE Conference on Decision and Control, Seville Spain,2005,3255-3260.
32. Farahmand A M, Yazdanpanah M J. Locally optimal Takagi-Sugeno fuzzy controllers[C]. IEEE Conference on Decision and Control, Seville Spain,2005,4095-4099.
33. Joo M G, Lee J S. A Class of Hierarchical Fuzzy Systems With Constraints on the Fuzzy Rules[J]. IEEE Transactions on Fuzzy Systems,2005,13(2):194-203.
34. Zeng X J, Keane J A. Approximation capabilities of hierarchical fuzzy systems[J]. IEEE Transactions on Fuzzy Systems,2005,13(5):659-672.
35. Liu P Y. Mamdani fuzzy system:universal approximator to a class of random processes[J]. IEEE Transactions on Fuzzy Systems,2002,10(6):756-766.
36. Liu P Y, Li H X. Approximation of stochastic processes by T-S fuzzy systems[J]. Fuzzy Sets and Systems,2005,155:215-235.
37. Shimoda M. A natural interpretation of fuzzy sets and fuzzy relations[J]. Fuzzy Sets and Systems,2002,128(2):135-147.
38. Coletti G, Scozzafava R. Conditional probability, fuzzy sets, and possibility:a unifying view[J]. Fuzzy Sets and Systems,2004,144(1):227-249.
39.佟绍成.非线性系统的自适应模糊控制[M].北京:科学出版社,2006.
40. Golea N, Golea A, Benmahammed K. Fuzzy model reference adaptive control[J]. IEEE Transactions on Fuzzy Systems,2002,10(4):436-444.
41. Lee Y, Z_ ak S H. Uniformly ultimately bounded fuzzy adaptive tracking controllers for uncertain systems[J]. IEEE Transactions on Fuzzy Systems,2004,12(6):797-811.
42.张化光.模糊广义预测控制及其应用[J].自动化学报,1993,19(1):9-17.
43.李少远,李柠.复杂系统的模糊预测控制及应用[M],北京:科学出版社,2003.
44. Huang Y L, Lou H H, Gong J P, Edgar T F. Fuzzy model predictive control[J]. IEEE Transactions on Fuzzy Systems,2000,8(6):665-678.
45. Mollov S, Babu·ska R, Abonyi J, Verbruggen H B. E(?)ective optimization for fuzzy model predictive control[J]. IEEE Transactions on Fuzzy Systems,2004,12(5):661-675.
46. Yang Y S, Ren J S. Adaptive fuzzy robust tracking controller design via small gain approach and its application[J]. IEEE Transactions on Fuzzy Systems,2003,11(6): 783-795.
47. Yang Y S, Zhou C J. Adaptive fuzzy H2 stabilization for strict-feedback canonical nonlinear systems via backstepping and small-gain approach[J]. IEEE Transactions on Fuzzy Systems,2005,13(1):104-114.
48. Chen B, Liu X P. Fuzzy approximate disturbance decoupling MIMO nonlinear systems by backstepping application to chemical processes[J]. IEEE Transactions on Fuzzy Systems,2005,13(6):832-847.
49. Boyd S, Ghauoi L E, Feron E, Balakrishan V. Linear matrix inequalities in system and control theory[M]. Philadelphia, PA:SIAM,1994.
50. Tanaka K,Wang H O. Fuzzy control systems design and analysis:a linear matrix inequality approach[M]. John Wiley & Sons, Inc.2001.
51. Fridman E, Shaked U. Delay-dependent stability and H2 control:constant and time-varying delays[J]. International Journal of Control,2003,76(1):48-60.
52. Gu K. Discretized LMI set in the stability problem for linear uncertain time-delay systems[J]. International Journal of Control,1997,68(4):923-934.
53. Han Q L. On stability of linear neutral systems with mixed time delays:A discretized Lyapunov functional approach[J]. Automatica,2005,41(7):1209-1218.
54. Han Q L, Gu K. Stability of linear systems with time-varying delay:a generalized discretized Lyapunov functional approach[J]. Asian Journal of Control,2001, 3(3):170-180.
55. Gu K, Niculescu S I. Additional dynamics in transformed time delay systems[J]. IEEE Transactions on Automatic Control,2000,45 (3):572-575.
56. Gu K. Niculescu S.I. Further remarks on additional dynamics in various model transformations of linear delay systems[J]. IEEE Transactions on Automatic Control, 2001,46 (3):497-500.
57. Fridman E. New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems[J]. Systems & Control Letters,2001,43(4):309-319.
58. Cao Y Y, Lam J, Sun Y X. Static output feedback stabilization:an LMI approach[J]. Automatica,1998,34(12):1641-1645.
59. Niculescu S I. On delay-dependent stability under model transformations neutral linear systems[J]. International Journal of Control,74(6):608-617.
60. Han Q L. Robust stability of uncertain delay-differential systems of neutral type[J]. Automatica,2002,38(4):718-723.
61. He Y, Wu M, She J H, et al. Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays[J]. Systems & Control Letters,2004,51(1):57-65.
62. Tseng C S. Model reference output feedback fuzzy tracking control design for nonlinear discrete-time systems with time-delay[J]. IEEE Transactions on Fuzzy Systems,2006, 14(1):58-70.
63. Chen S S, Chang Y C, Su S F, Chung S L, Lee T T. Robust static output feedback stabilization for nonlinear discrete-time systems with time delay via fuzzy control approach[J]. IEEE Transactions on Fuzzy Systems,2005,13(2):263-272.
64. Xu S Y, Lam J. Robust H∞ control for uncertain discrete-time-delay fuzzy systems via output feedback controllers[J]. IEEE Transactions on Fuzzy Systems,2005,13(1):82-93.
65. Lee K R, Kim J H, Jeung E T, Park H B. Output feedback robust H∞ control of uncertain fuzzy dynamic systems with time-varying delay[J]. IEEE Transactions on Fuzzy Systems, 2000,8(6):657-664.
66. Chen B S, Tseng C S, Uang H J. Mixed H2/H∞ Fuzzy Output Feedback Control Design for Nonlinear Dynamic Systems:An LMI Approach[J]. IEEE Transactions on Fuzzy Systems,2000,8(3):249-265.
67.杨冬梅,张庆灵,姚波等.广义系统[M].北京:科学出版社,2004.5.
68. Cobb J D. Controllability, observability, and duality in singular systems[J]. IEEE Transactions on Automatic Control,1984,29:572-588.
69. Bender D J, Laub A J. The linear-quadratic optimal regulation for descriptor systems[J]. IEEE Transactions on Automatic Control,1987,32(8):1076-1082.
70. Dai L. Singular Control Systems. Berlin:Spring-Verlag,1989.
71.张庆灵.广义大系统的分散控制与鲁棒控制[M].西安:西北工业大学出版社,1997.
72.刘永清,谢湘生.滞后广义系统解的稳定镇定与控制[M].1998.
73.徐胜元.广义不确定系统的鲁棒控制.南京理工大学博士论文,1999.
74. Xu S Y, Dooren P V, Stefan R, et al. Robust Stability and Stabilization for Singular Systems With State Delay and Parameter Uncertainty[J]. IEEE Trans. On Automatic Control,2002,47(7):1122-1128.
75.董心壮,张庆灵.滞后广义系统的状态反馈H∞控制[J].控制理论与应用,2004,21(6):941-944.
76.杨帆,张庆灵.不确定广义变时滞系统输出反馈H∞控制[J].东北大学学报(自然科学版),2005,26(1):217-220.
77.舒伟仁,张庆灵.时滞区间广义系统的鲁棒非脆弱H∞控制器[J].电机与控制学报,2005,9(2):119-123.
78.付兴建,童朝南.基于LMI的奇异不确定时滞系统鲁棒保成本控制[J].电机与控制学报,2005,9(5):491-494.
79. Feng J, Zhang W, Cheng Z, et al.H∞ output feedback control for descriptor systems with delayed-state[C]. American Control Conference, Porland,OR, USA,2005,4892-4896.
80. Zhu S, Li Z, Cheng Z. Delay-dependent robust resilient H∞ control for uncertain singular time-delay systems[C]. Proceedings of the 44th IEEE Conference on Decision and Control, and the Euroupean Control Conference, Seville,Spain,2005,1373-1378.
81.朱宝彦.一类T-S模糊广义系统的分析与控制[D],沈阳,东北大学,2006.
82. Taniguchi T, Tanaka K, Yamafuji K, et al. Fuzzy descriptor systems:stability analysis and design via LMIs[C]. Proc. American Control Conference, San Diago, CA,1999, 1827-1831.
83. Taniguchi T, Tanaka K, Wang H O. Fuzzy descriptor systems and fuzzy controller designs[C]. Proc. of the 8th International Fuzzy System Association World Congress, Taipei,Taiwan,1999,655-659.
84. Yoneyama J, Ichikawa A.H∞ control for Takagi-Sugeno fuzzy descriptor systems[C]. Proc. IEEE Conf. Systems, Man and Cybernetics,1999,111-28-111-33.
85. Taniguchi T, Tanaka K, Wang H O. Fuzzy descriptor systems and nonlinear model following control[J]. IEEE Trans.on Fuzzy Systems,2000,8(4):442-432.
86. Wang Y, Zhang Q L, Liu W Q. Stability analysis and design for T-S fuzzy descriptor systems[C]. Proceedings of the 40th IEEE conference on Decision and Control, Orlando, Florida USA,2001,3962-3967.
87.刘晓东,张庆灵,王岩.T-S模糊广义系统的H∞控制[J].东北大学学报(自然科学版),2002,23(5):429-431.
88.时晓岩,高志伟.模糊广义系统的稳定性分析与控制器设计[J].天津大学学报,2004,37(9):806-809.
89.朱宝彦,张庆灵.参数不确定的广义T-S模糊系统的最优保成本控制[J].系统工程理论与实践,2004,12:49-57.
90. Wang Y, Sun Z Q, Sun F C. Robust fuzzy control of a class of nonlinear descriptor systems with time-varying delay[J]. International Journal of Control, Automation, and Ststems,2004,2(1):76-82.
91.朱宝彦,张庆灵.时滞T-S模糊广义系统鲁棒H∞控制[J].电机与控制学报,2005,9(4):352-356.
92. Huang C P. Stability analysis of discrete singular fuzzy systems[J]. Fuzzy Set and Systems,2005,151:155-165.
93. Lin C, Wang Q G, Lee T H. Stability and stabilization of a class of fuzzy time-delay descriptor systems[J]. IEEE Transactions on Fuzzy Systems,2006,14(4):542-551.
94.朱宝彦,张庆灵,张雪峰.参数不确定T-S模糊交联系统的分散保成本控制[J].控制与决策,2005,20(9):986-991.
95.袁宇浩,张庆灵,陈兵.非线性广义系统时滞相关的模糊控制[J].自动化学报,2006,32(5):824-828.
96.张友刚,胥布工,候晓丽.参数不确定性模糊大系统的保性能控制:LMI方法[J].华南理工大学学报(自然科学版),2006,34(1):66-72.
97.黄剑,关治洪,王仲东.不确定离散脉冲系统的保成本控制研究[J].华中科技大学学报(自然科学版),2006,34(2):84-86.
98.孙文安,冯佳昕,付俊等.一类不确定离散系统的混杂状态反馈二次保成本控制[J].东北大学学报(自然科学版),2005,26(11):1021-1024.
99.汪锐,孙文安,齐丽等.一类线性不确定切换系统的保成本鲁棒控制[J].东北大学学报(自然科学版),2005,26(4):213-215.
100.Meng B, Zhang J F. Output feedback based admissible control of switched linear singular system[J]. ACTA Automatica Sinica,2006,32(2):179-184.
101.Lee Y S, Moon Y S, Kwon W H. Delay-dependent guaranteed cost control for uncertain state-delay systems[C]. Proceedings of American Control Conference, Arlington, VA: AACC,2001:3376-3381.
102.Chen B, Liu X P. Fuzzy Guaranteed cost control for nonlinear systems with time-varying delay[J]. IEEE Transactions on Fuzzy Systems,2005,13(2):238-249.
103.Xie L, de Souza C E. Robust H8 control for linear systems with norm-bounded time-varying uncertainty[J]. IEEE Transactions on Automatic Control,1992,37(8): 1188-1191.
104.Chen B, Liu X P. Reliable control design of fuzzy dynamic systems with time-varying[J]. Fuzzy Sets and Systems,2004,146(5):349-374.
105.Ma B P, Zhu X M, Sun J. Guaranteed cost control of uncertain T-S fuzzy descriptor systems[C]. Proceedings of Fourth International Conference om Machine Learning and Cybernetics, Guangzhou, China,2005:742-746.
106.Wang Y, Xie L, de Souza C E. Robust control of a class of uncertain nonlinear systems[J]. System Control Letters,1992,19:139-149.
107.Yu L Optimal guaranteed cost control for uncertain discrete-time linear systems[J]. Control Theory and Applications,1999,16(5):639-642.
108.Moon Y S. Delay-dependent robust stabilization of uncertain state-delayed systems[J]. Int. J. Control,2001,74:1447-1455.
109.Guan X P, Chen C L. Delay-dependent guaranteed cost control for T-S fuzzy systems with time delays[J]. IEEE Transactions on Fuzzy Systems,2004,12(2):236-249.
110.Wu H N, Li H X. New approach to delay-dependent stability analysis and stabilization for continuous-time fuzzy systems with time-varying delay[J]. IEEE Transactions on Fuzzy Systems,2007,15(3):482-493.
111.Zhu S Q, Zhang C H, Cheng Z L, et al. Delay-dependent robust stability criteria for two classes of uncertain singular time delay systems[J]. IEEE Transactions on Automatic Control,2007,52(5):880-885.
112.肖伸平,吴敏,张先明.不确定时滞系统的时滞相关非脆弱鲁棒H∞控制[J].系统科学与数学,2007,27(3):401-411.
113.Yang G H, Wang J L. Non-fragile H∞ control for linear systems with multi plicative controller gain variations[J]. Automatica,2001,37(5):727-737.
114.Xu S Y, Lam J, Wang J L, Yang G H. Non-fragile positive real control for uncertain linear neutral delay systems[J]. Systems & Control Letters,2004,52(1):59-74.
115.Chen B, Liu X P. Delay-dependent robust H∞ control for T-S fuzzy systemswith time delay[J]. IEEE Transactions on Fuzzy Systems,2005,13(4):544-556.
116.Yoneyama J. Design of H∞-control for time-delay systems[J]. Fuzzy Sets and Systems, 2005,151:167-190.
117.Hsiao F H, Hwang J D, Chen C W, Tsai Z R. Robust stabilization of nonlinear multiple time-delay large-scale systems via decentralized fuzzy control[J]. IEEE Transactions on Fuzzy Systems,2005,13(1):152-163.
118.Wang W J, Lin W W. Decentralized PDC for large-scale T-S fuzzy systems[J].IEEE Transactions on Fuzzy Systems,2005,13(6):779-786.
119.Wang Y, Zhang Q L, Liu X D. Robustness design of uncertain discrete-time fuzzy descriptor system with guaranteed admissibility[C]. Proc. American Control Conference, AACC,2002:1699-1704.
120.Yang M, JingY W. Robust stabilization of nonlinear time delay discrete time systems based on T-S model[J]. ACTA Automatica Sinica,2006,32(2):207-212.
121.巩长忠,王伟,刘全利.基于观测器的非线性不确定离散系统的鲁棒模糊控制[J].控制理论与应用,2005,22(1):96-100.
122.陈跃鹏,周祖德,刘焕彬等.离散广义系统具有完整性的鲁棒二次稳定[J].控制理论与应用,2006,23(1):14-18.
123.Zhang S, Ren G. Stability analysis of discrete T-S fuzzy systems with piecewise fuzzy Lyapunov approach[C]. Proceedings of the 6th Word Congress on Intelligent Control and Automation, Dalian, China,2005:3796-3800.
124.Lee H J, Kau S W, Lee C H, et al. H∞ Control for discrete-time fuzzy descriptor systems[C]. IEEE International Conference on Systems, Man and Cybernetics, Taipei, Taiwan,2006:5059-5064.
125.Dong J X, Yang G H. Static output feedback control synthesis for discrete-time T-S fuzzy systems[J]. International Journal of Control, Automation, and Systems,2007,5(3): 349-354.
126.Mahmoud M S. New results on robust control design of discrete-time uncertain systems[J]. IEE Proceedings:Control Theory and Applications,2005,152(4):453-459.
127.Wang W J, Luoh L. Stability and stabilization of fuzzy largescale systems[J].IEEE Transactions on Fuzzy Systems,2004,12(3):309-315.
128.Zhang H B, Li C G, Liao X F. Stability analysis and H∞ controller design of fuzzy large-scale systems based on piecewise lyapunov functions[J]. IEEE Transactions on Systems, Man, and Cybernetics, Part B:Cybernetics,2006,36(3):685-698.
129.Wu H N, Zhang H Y. Reliable mixed fuzzy static output feedback control for nonlinear systems with sensor faults[J]. Automatica,2005,41(4):1925-1932.
130.Wu H N. Reliable LQ fuzzy control for continuous-time nonlinear systems with actuator faults[J]. IEEE Transactions on Systems, Man, and Cybernetics, Part B:Cybernetics, 2004,34(4):1743-1752.