Finite-time H∞ Control for Uncertain System With Time-varying Delay and Exogenous Disturbance

This paper is concerned with the problems of finite-time boundedness and finite-time H∞ control for a class of uncertain systems with time-varying delays and exogenous disturbance. By using appropriately chosen Lyapunov-Krasovskii functional (LKF), together with the new integral inequality, new sufficient conditions of finite-time boundedness (FTB) for uncertain time-delay systems are given in terms of linear matrix inequalities (LMIs). Then, by designing the output feedback controller, we established new sufficient conditions to guarantee that the closed-loop system is finite-time bounded with H∞ performance index. The desired controller gain matrix can be obtained by solving the obtained LMIs. Furthermore, we give a criterion of finite-time stability for the closed-loop system without external disturbance based on the output feedback control. Finally, some numerical examples are given to illustrate the effectiveness of the proposed methods.