Aperiodic Sampled-Data H_∞ Filtering for Lipschitz Nonlinear Systems: An Impulsive System Approach

Abstract

This paper is concerned with the $H_{\infty }$ filtering for Lipschitz nonlinear systems under aperiodically sampled measurements. The developed filter is a hybrid system, whose states undergo a change or reset at sampling instants. The resulting filtering error system is then modelled as a kind of nonlinear impulsive systems. By introducing a time-varying Lyapunov functional candidate, a sufficient condition for the existence of desired filter is derived to ensure the filtering error system asymptotic stability and guarantee an $H_{\infty }$ performance. The optimal $H_{\infty }$ performance and corresponding filter gain matrix can be obtained by solving a convex problem with linear matrix inequalities (LMIs) constrains. Two examples are given to show the effectiveness of the theoretical results, and our results are less conservative than existing ones through comparisons.

Keywords

• Lipschitz nonlinear systems
• sampled-data filtering
• H∞ performance
• impulsive system approach