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Delay-Dependent Robust \hbox {\it H}_\infty Control for Uncertain Discrete-Time Fuzzy Systems With Time-Varying Delays

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2 Author(s)
Baoyong Zhang ; Sch. of Autom., Nanjing Univ. of Sci. & Technol., Nanjing, China ; Shengyuan Xu

This paper deals with the robust H infin control problem for discrete-time Takagi-Sugeno (T-S) fuzzy systems with norm-bounded parametric uncertainties and interval time-varying delays. First, based on a new Lyapunov functional, we present a sufficient condition guaranteeing that the resulting closed-loop system is robustly stable and satisfies a prescribed H infin performance level. The Lyapunov functional used here depends on not only the fuzzy basis function but on the lower and upper bounds of the time-varying delay as well. Second, two classes of delay-dependent conditions for the existence of the concerned H infin fuzzy controllers are given in terms of relaxed linear matrix inequalities (LMIs), and a desired controller can be designed by using the solutions to these LMIs. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed design method.

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Fuzzy Systems, IEEE Transactions on  (Volume:17 ,  Issue: 4 )