Finite-Time Control for Nonlinear Systems with Time-Varying Delay and Exogenous Disturbance

Abstract

This paper is concerned with the problem of finite-time control for nonlinear systems with time-varying delay and exogenous disturbance, which can be represented by a Takagi−Sugeno (T-S) fuzzy model. First, by constructing a novel augmented Lyapunov−Krasovskii functional involving several symmetric positive definite matrices, a new delay-dependent finite-time boundedness criterion is established for the considered T-S fuzzy time-delay system by employing an improved reciprocally convex combination inequality. Then, a memory state feedback controller is designed to guarantee the finite-time boundness of the closed-loop T-S fuzzy time-delay system, which is in the framework of linear matrix inequalities (LMIs). Finally, the effectiveness and merits of the proposed results are shown by a numerical example.

Keywords

• finite-time boundedness
• t-s fuzzy systems
• time-varying delay
• lyapunov–krasovskii functional (lkf)