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Delay-dependent robust $$H_\infty$$ control for T-S fuzzy system with interval time-varying delay. (English) Zbl 1175.93134
Summary: This paper is concerned with the problem of robust $$H_\infty$$ control for uncertain T-S fuzzy systems with interval time-varying delay, that is, the delay is assumed to be a time-varying function belonging to an interval. By defining new Lyapunov functions and making use of novel techniques to achieve delay dependence, new conditions for the existence of robust $$H_\infty$$ controllers are obtained based on the Parallel Distributed Compensation (PDC) method. In this article, all the conditions are shown in terms of Linear Matrix Inequalities (LMIs), which can be solved efficiently by using the LMI optimization techniques. Two numerical examples are given to illustrate the less conservatism of the proposed method.

##### MSC:
 93C42 Fuzzy control/observation systems 93B36 $$H^\infty$$-control 93B35 Sensitivity (robustness) 93C41 Control/observation systems with incomplete information
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