×

Stability analysis of T-S fuzzy models for nonlinear multiple time-delay interconnected systems. (English) Zbl 1049.93556

Summary: The Takagi-Sugeno (T-S) fuzzy model representation is extended to the stability analysis for nonlinear interconnected systems with multiple time-delays using linear matrix inequality (LMI) theory. In terms of Lyapunov’s direct method for multiple time-delay fuzzy interconnected systems, a novel LMI-based stability criterion which can be solved numerically is proposed. Then, the common \(P\) matrix of the criterion is obtained by LMI optimization algorithms to guarantee the asymptotic stability of nonlinear interconnect systems with multiple time-delay. Finally, the proposed stability conditions are demonstrated with simulations throughout this paper.

MSC:

93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93C42 Fuzzy control/observation systems
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Lee, C. H.; Li, T. H.; Kung, F. C., On the robust stability for continuous large-scale uncertain systems with time delays in interconnections, J. Chin. Inst. Eng., 17, 577-584 (1994)
[2] S.G. Tzafestas, K. Watanabe, Stochastic Large-Scale Engineering Systems, Marcel Dekker, New York, 1992.; S.G. Tzafestas, K. Watanabe, Stochastic Large-Scale Engineering Systems, Marcel Dekker, New York, 1992. · Zbl 0842.00027
[3] M.S. Mahmoud, M.F. Hassan, M.G. Darwish, Large-Scale Control Systems, Marcel Dekker, New York, 1985.; M.S. Mahmoud, M.F. Hassan, M.G. Darwish, Large-Scale Control Systems, Marcel Dekker, New York, 1985. · Zbl 0628.93001
[4] Yan, X. G.; Dai, G. Z., Decentralized output feedback robust control for nonlinear large-scale systems, Automatica, 34, 1469-1472 (1998) · Zbl 0934.93007
[5] Trinh, H.; Aldeen, M., A comment on decentralized stabilization of large scale interconnected systems with delays, IEEE Trans. Automat. Contr., 40, 914-916 (1995) · Zbl 0825.93629
[6] Cao, Y. Y.; Frank, P. M., Stability analysis and synthesis of nonlinear time-delay systems via linear Takagi-Sugeno fuzzy models, Fuzzy Sets Syst., 124, 213-229 (2001) · Zbl 1002.93051
[7] Mori, T., Criteria for asymptotic stability of linear time delay systems, IEEE Trans. Automat. Contr., 30, 158-162 (1985) · Zbl 0557.93058
[8] Takagi, T.; Sugeno, M., Fuzzy identification of systems and its applications to modeling and control, IEEE Trans. Syst. Man Cybern., 15, 116-132 (1985) · Zbl 0576.93021
[9] S. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, PA, 1994.; S. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, PA, 1994. · Zbl 0816.93004
[10] Y. Nesterov, A. Nemirovsky, Interior-Point Polynomial Methods in Convex Programming, SIAM, Philadelphia, PA, 1994.; Y. Nesterov, A. Nemirovsky, Interior-Point Polynomial Methods in Convex Programming, SIAM, Philadelphia, PA, 1994. · Zbl 0824.90112
[11] Park, C. W.; Kang, H. J.; Yee, Y. H.; Park, M., Numerical robust stability analysis of fuzzy feedback linearisation regulator based on linear matrix inequality approach, IEEE Proc. Contr. Theory Appl., 149, 1-10 (2002)
[12] Wang, H.; Tanaka, O. K.; Griffin, M. F., An approach to fuzzy control of nonlinear systems: stability and design issues, IEEE Trans. Fuzzy Syst., 4, 14-23 (1996)
[13] Feng, G.; Cao, S. G.; Rees, N. W.; Chak, C. K., Design of fuzzy control systems with guaranteed stability, Fuzzy Sets and Syst., 85, 1-10 (1997) · Zbl 0925.93508
[14] Zhou, K.; Khargonedkar, P. P., Robust stabilization of linear systems with norm-bounded time-varying uncertainty, Syst. Contr. Lett., 10, 17-20 (1988) · Zbl 0634.93066
[15] Tanaka, K.; Ikeda, T.; Wang, H. O., Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stabilizability, \(H^∞\) control theory, and linear matrix inequalities, IEEE Trans. Fuzzy Syst., 4, 1-13 (1996)
[16] Lu, L. T.; Chiang, W. L.; Tang, J. P., Application of model reduction and LQG/LTR robust control methodology in active structure control, ASCE J. Eng. Mech., 124, 446-454 (1998)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.