Delay-dependent generalized H₂ control for discrete T-S fuzzy large-scale stochastic systems with mixed delays

• Autorzy: Jiangrong Li , Junmin Li , Zhile Xia
• Języki publikacji: EN

Abstrakty

EN

This paper is concerned with the problem of stochastic stability and generalized H₂ control for discrete-time fuzzy largescale stochastic systems with time-varying and infinite-distributed delays. Large-scale interconnected systems consist of a number of discrete-time interconnected Takagi-Sugeno (T-S) subsystems. First, a novel Delay-Dependent Piecewise Lyapunov-Krasovskii Functional (DDPLKF) is proposed, in which both the upper and the lower bound of delays are considered. Then, two improved delay-dependent stability conditions are established based on this DDPLKF in terms of Linear Matrix Inequalities (LMIs). The merit of the proposed conditions lies in its reduced conservatism, which is achieved by circumventing the utilization of some bounding inequalities for cross products of two vectors and by considering the interactions among the fuzzy subsystems in each subregion. A decentralized generalized H₂ state feedback fuzzy controller is designed for each subsystem. It is shown that the mean-square stability for discrete T-S fuzzy large-scale stochastic systems can be established if a DDPLKF can be constructed and a decentralized controller can be obtained by solving a set of LMIs. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed method.

Słowa kluczowe

EN

fuzzy large-scale stochastic system; delay-dependent; generalized H₂ control; infinite-distributed delays; linear matrix inequality

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2011
• Tom: 21
• Numer: 4
• Strony: 585-603

Daty

wydano

2011

otrzymano

2010-09-29

poprawiono

2011-03-23

Twórcy

autor

Jiangrong Li

• School of Science, Xidian University, South Taibai Rd 2, Xi'an, 710071, PR China
• College of Mathematics and Computer Science, Yanan University, Yangjialing, Yan'an, 716000, PR China

autor

Junmin Li

• School of Science, Xidian University, South Taibai Rd 2, Xi'an, 710071, PR China

autor

Zhile Xia

• School of Mathematics and Information Engineering, Taizhou University, Shifu Rd 1139, Taizhou, 317000, PR China

Bibliografia

• Chen, M. and Feng, G. (2008). Delay-dependent $H_∞$ filter of piecewise-linear systems with time-varying delays, IEEE Transactions on Circuits and Systems, I: Regular Papers 55(7): 2087-2095.
• Chen, M., Feng, G. and Ma, H.B. (2009). Delay-dependent $H_∞$ filter design for discrete-time fuzzy systems with time-varying delays, IEEE Transactions on Fuzzy Systems 17(3): 604-616.
• Dong, H.L., Wang, Z.D. and Gao, H.J. (2010). Robust $H_∞$ filter for a class of nonlinear networked systems with multiple stochastic communication delays and packet dropouts, IEEE Transactions on Signal Processing 58(4): 1957-1966.
• Gao, H.J., Lam, J. and Wang, Z.D. (2007a). Discrete bilinear stochastic systems with time-varying delay: Stability analysis and control synthesis, Chaos, Solitons and Fractals 34(2): 394-404.
• Gao, H.J. and Chen, T.W. (2007b). New results on stability of discrete-time systems with time-varying state delay, IEEE Transactions on Automatic Control 52(2): 328-334.
• Gao, H.J., Liu, X.M. and Lam, J. (2009a). Stability analysis and stabilization for discrete-time fuzzy systems with timevarying delay, IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 39(2): 306-317.
• Gao, H.J., Zhao, Y. and Chen, T.W. (2009b). $H_∞$ fuzzy control of nonlinear systems under unreliable communication links, IEEE Transactions on Fuzzy Systems 17(2): 265-277.
• Gong, Ch. and Su, B.K. (2009). Delay-dependent robust stabilization for uncertain stochastic fuzzy system with timevarying delays, International Journal of Innovative Computing, Information and Control 5(5): 1429-1440.
• Guerra, T.M. and Vermeiren, L. (2004). LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the Takagi-Sugeno form, Automatica 40(5): 823-829.
• Halabi, S., Souley Ali, H., Rafaralahy, H. and Zasadzinski, M. (2009). $H_∞$ functional filtering for stochastic bilinear systems with multiplicative nosies, Automatica 45(4): 1038-1045.
• Johansson, M, Rantzer, A., and Arzen, K.E. (1999). Piecewise quadratic stability of fuzzy systems, IEEE Transactions on Fuzzy Systems 7(6): 713-722.
• Lam, H.K. (2008). Stability analysis of T-S fuzzy control systems using parameter-dependent Lyapunov function, IET Control Theory and Applications 3(6): 750-762.
• Li, H.Y., Chen, B., Zhou, Q. and Qian, W.Y. (2009). Robust stability for uncertain delayed fuzzy hopfield neural networks with markovian jumping parameters, IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 39(1): 94-102.
• Li, H.Y., Wang, C., Shi, P. and Gao, H.J. (2010). New passivity result for uncertain discrete-time stochastic neual networks with mixed time delays, Neurocomputing 73(16-18): 3291-3299.
• Qiu, J.B., Feng, G. and Yang, J. (2009). A new design of delaydependent robust $H_∞$ filtering for discrete-time T-S fuzzy systems with time-varying delay, IEEE Transcations on Fuzzy Systems 17(5): 1044-1058.
• Takagi, T. and Sugeno, M. (1985). Fuzzy identification of systems and its applications to modeling and control, IEEE Transactions on Systems, Man and Cybernetics-Part B: Cybernetics 15(1): 116-132.
• Tong, S.H., Liu, C.L. and Li, Y.M. (2010). Fuzzy-adaptive decentralized output-feedback control for large-scale nonlinear systems with dynamical uncertainities, IEEE Transactions on Fuzzy Systems 18(5): 845-861.
• Tseng, C.S. (2009). A novel approach to $H_∞$ decentralized fuzzy-observer-based fuzzy control design for nonlinear interconnected systems, IEEE Transactions on Fuzzy Systems 17(1): 233-242.
• Wang, W.J., Chen, Y.J. and Sun, C.H. (2007). Relaxed stabiliza tion criteria for discrete-time T-S fuzzy control systems based on a swithching fuzzy model and piecewis Lyapunov function, IEEE Transactions on Systems, Man and Cybernetics, Part B: Cybernetics 37 (3): 551-559.
• Wang, Z.D., Liu, Y.R., Wei, G.L. and Liu, X.H. (2010). A note on control of a class of discrete-time stochastic systems with distributed delays and nonlinear disturbances, Automatica 46(3): 543-548.
• Wang, L., Feng, G. and Hesketh, T. (2004). Piecewise generalized H₂ controller synthesis of discrete-time fuzzy systems, IEE Proceedings: Control Theory and Applications 51(9): 554-560.
• Wang, Y., Gong, C., Su, B.K. and Wang, Y.J. (2009). Delaydependent robust stabilization of uncertain T-S fuzzy system with time-varying delays, International Journal of Innovative Computing, Information and Control 5(9): 2665-2674.
• Wang, C. (2010). Stability analysis of T-S discrete fuzzy largscale systems, ICIC Express Letters 4(4): 1287-1293.
• Wei, G.L., Feng, G. and Wang, Z.D. (2009). Robust $H_∞$ control for discrete-time fuzzy systems with infinite-distributed delays, IEEE Transactions on Fuzzy Systems 17(1): 224-232.
• Wu, L.G. and Daniel, W.C.H. (2008). Fuzzy filter design for Itô stochastic systems with application to sensor fault detection, IEEE Transactions on Fuzzy Systems 16(5): 1337-1350.
• Zhang, H.B., Li, C.G. and Liao, X.F. (2006). Stability analysis and $H_∞$ controller design of fuzzy large-scale systems based on piecewise Lyapunov functions, IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics 36(3): 685-698.
• Zhang, H.B., Dang, C.Y. and Li, C.G. (2008a). Stability analysis and $H_∞$ controller design of discrete-time fuzzy largescale systems based on piecewise Lyapunov functions, IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 38(5): 1390-1401.
• Zhang, H.B. and Dang, C.Y. (2008b). Piecewise $H_∞$ controller design of uncertain discrete-time fuzzy systems with time delays, IEEE Transactions on Fuzzy Systems 16(6): 1649-1655.
• Zhang, H.B., Dang, C.Y. and Li, C.G. (2009a). Decentralized $H_∞$ filter design for discrete-time interconnected fuzzy systems, IEEE Transactions on Fuzzy Systems 17(6): 1428-1440.
• Zhang, H.B., Feng, G. and Dang, C. (2009b). Stability analysis and $H_∞$ control for uncertain stochastic piecewiselinear systems, IET Control Theory and Applications 3(8): 1059-1069.
• Zhang, H.B., Dang, C.Y. and Zhang, J. (2010). Decentralized fuzzy $H_∞$ filtering for nonlinear interconnected systems with multiple time delays, IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 40(4): 1197-1202.
• Zhang, S.Y. (1985). Decentralized stabilization of dynamically interconnected systems, Systems and Control Letter 6(1): 47-51.
• Zhang, W., Wang, T. and Tong, S.C. (2009). Delaydependent stabilization conditions and control of T-S fuzzy systems with time-delay, ICIC Express Letters 3(4): 871-876.

Identyfikatory

DOI

10.2478/v10006-011-0046-6