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Robust H∞ control for uncertain T-S fuzzy systems via delay partitioning approach

S. Idrissi, E.H. Tissir, I. Boumhidi, Nourddine Chaibi

Abstract


This paper discusses the problem of robust H∞ control for uncertain T–S fuzzy systems with interval time-varying delay. The approach is based on constructing a new Lyapunov-Krasovskii functional by dividing uniformly the delay interval into N segment with N is a positive integer and some free weighting matrices. This new Lyapunov-Krasovskii functional is chosen with different weighted matrices corresponding to different segments. Based on this approach and the parallel distribution compensation (PDC) method, new conditions of robust H∞ control are presented. The perturbations considered are norm bounded, and the results are expressed in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, an H∞ controller is obtained. Finally, numerical examples show that the proposed method is less conservative than existing ones.

Keywords


Delay dependent stability, H∞ control, T-S fuzzy systems, Robust control, Uncertainty, Liner matrix inequalities (LMIs).

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