Guaranteed cost control for uncertain fuzzy systems with time-delay

Abstract

A guaranteed cost control method for nonlinear systems with time-delay is introduced in this paper, which can be represented by Takagi-Sugeno (T-S) fuzzy models with time-delays. The state feedback approach is considered. By introducing a new Lyapunov-Krasovskii functional with adjustable parameters, and based on delay-dependent stability analysis, some sufficient conditions for the existence of state feedback controller via parallel distributed compensation (PDC) are given in the form of linear matrix inequalities (LMIs). The different guaranteed cost and different feedback gains are gotten by choosing different adjustable parameters. Different feedback gains lead to different dynamic performance of closed-loop systems, therefore, the optimal dynamic performance of closed-loop systems can be gotten by choosing proper adjustable parameters. The guaranteed cost can be regarded as the function of adjustable parameters, and an algorithm is given to get the minimum of the guaranteed cost. The effectiveness of the proposed method can be illustrated by the simulation example.