Delay-dependent generalized H 2 fuzzy static-output-feedback control for discrete T-S fuzzy bilinear stochastic systems with mixed delays

Abstract

This paper is concerned with the delay-dependent generalized H₂ fuzzy static out feedback control scheme for a class of nonlinear systems with mixed time delays. The nonlinear plant is represented by Takagi-Sugeno (T-S) fuzzy bilinear stochastic systems with time-varying and infinite-distributed delays. Firstly, a novel delay-dependent piecewise Lyapunov-Krasovskii functional (DDPLKF) is proposed, in which both the upper and the lower bound of delays are considered. Then, based on this DDPLKF, a new delay-dependent generalized H₂ fuzzy static output feedback controller design approach is first derived for the fuzzy bilinear stochastic system, and two improved delay-dependent stochastic stability conditions are established. The solutions of the problem can be obtained by solving a set of nonlinear minimization problems involving linear matrix inequalities (LMIs) constraints. An iterative algorithm making use of sequential linear programming matrix method (SLPMM) is proposed to solve the nonlinear minimization problem. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed approaches in this paper.