Robust Finite‐TimeH_∞Control for Impulsive Switched Nonlinear Systems with State Delay

Abstract

This paper investigates robust finite‐time H ∞ control for a class of impulsive switched nonlinear systems with time‐delay. Firstly, using piecewise Lyapunov function, sufficient conditions ensuring finite‐time boundedness of the impulsive switched system are derived. Then, finite‐time H ∞ performance analysis for impulsive switched systems is developed, and a robust finite‐time H ∞ state feedback controller is proposed to guarantee that the resulting closed‐loop system is finite‐time bounded with H ∞ disturbance attenuation. All the results are given in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are provided to show the effectiveness of the proposed method.