Delay-dependent Robust Stabilization for Uncertain T-S Fuzzy Systems with Additive Time Varying Delays

Abstract

This paper investigates the problem of robust stabilization for uncertain Takagi–Sugeno (T–S) fuzzy systems with additive time varying delays. An appropriate Lyapunov-Krasovskii function is considered for solving this problem, and obtains considerably less conservative results than existing methods. The proposed approach constructs a new Lyapunov-Krasovskii functional using two additive delay components, and no free weighting matrices are employed in the theoretical result derivation. This reduces the number of scalar decision variables in linear matrix inequalities. The fuzzy state feedback gain is derived through the numerical solution of a set of linear matrix inequalities (LMIs). Finally, numerical examples are provided to illustrate the effectiveness of the proposed method, and to allow comparison with previous works.