DOI: 10.3724/SP.J.1004.2009.00328

Acta Automatica Sinica (自动化学报) 2009/35:3 PP.328-331

Passive Controller Design for T-S Fuzzy Systems with Time-delay

A sufficient condition is derived for the existence of passive state feedback controller for T-S fuzzy systems with time-delay. Compared with the existing results, this condition is less conservative. Based on this result, sufficient conditions are given for the existence of observer-based controller and dynamic output feedback controller. The controllers are designed by solving a set of linear matrix inequalities (LMIs). Finally, two illustrative examples are given to show the validity of the proposed approaches.

Key words:T-S fuzzy systems with time-delay, passive control, linear matrix inequality (LMI)

ReleaseDate:2014-07-21 14:32:46

Funds:Supported by National Natural Science Foundation of China (60574011)

1 Willems J C, Trentelman H L. Synthesis of dissipative systems using quadratic differential forms: part I. IEEE Transactions on Automatic Control, 2002, 47(1): 53-69

2 Takagi T, Sugeno M. Fuzzy identification of systems and its applications to modeling and control. IEEE Transactions on Systems, Man, and Cybernetics, 1985, 15(1): 116-132

3 Liu X D, Zhang Q L. Approaches to quadratic stability conditions and H∞ control designs for T-S fuzzy systems. IEEE Transactions on Fuzzy Systems, 2003, 11(6): 830-839

4 Uang H J. On the dissipativity of nonlinear systems: fuzzy control approach. Fuzzy Sets and Systems, 2005, 156(2): 185-207

5 Li C G, Zhang H B, Liao X F. Passivity and passification of uncertain fuzzy systems. IEE Proceedings Circuits, Decices and Systems, 2005, 152(6): 649-653

6 Liu X W. Passivity analysis of uncertain fuzzy delayed systems. Chaos, Solitons and Fractals, 2007, 34(3): 833-838

7 Zhu Bao-Yan. Analysis and Control for a Kind of T-S Fuzzy Descriptor Systems [Ph.D. dissertation], Northeastern University, China, 2006 (朱宝彦. 一类T-S模糊广义系统的分析与控制[博士学位论文], 东北大学, 中国, 2006)

8 Zhu Bao-Yan, Zhang Qing-Ling, Tong Shao-Cheng. Passivity control for uncertain T-S fuzzy descriptor systems. Acta Automatica Sinica, 2006, 32(5): 674-679 (朱宝彦, 张庆灵, 佟绍成. 不确定T-S模糊广义系统的无源控制.自动化学报, 2006, 32(5): 674-679)

9 Sun W Q, Khargonekr P P, Shim D. Solution to the positive real control problem for linear time-invariant systems. IEEE Transactions on Automatic Control, 1994, 39(10): 2034-2046

10 Liu X D, Zhang Q L. New approaches to H∞ controller design based on fuzzy observers for T-S fuzzy systems via LMI. Automatica, 2003, 39(9): 1571-1582