Nonfragile Robust Finite-Time L 2 - L ∞ Controller Design for a Class of Uncertain Lipschitz Nonlinear Systems with Time-Delays

Abstract

The nonfragile robust finite-time $L_2$-$L_{\infty }$ control problem for a class of nonlinear uncertain systems with uncertainties and time-delays is considered. The nonlinear parameters are considered to satisfy the Lipschitz conditions and the exogenous disturbances are unknown but energy bounded. By using the Lyapunov function approach, the sufficient condition for the existence of nonfragile robust finite-time $L_2$-$L_{\infty }$ controller is given in terms of linear matrix inequalities (LMIs). The finite-time controller is designed such that the resulting closed-loop system is finite-time bounded for all admissible uncertainties and satisfies the given $L_2$-$L_{\infty }$ control index. Simulation results illustrate the validity of the proposed approach.