L2‐L∞ filtering for a class of stochastic nonlinear systems with aperiodic sampling

Abstract

This work investigates the problem of L2‐L∞ filtering for a class of stochastic nonlinear systems with nonuniform sampling. The sampled‐data filter developed in this paper is an impulsive differential system whose states change abruptly at every sampling instant. The resulting filtering error system is modeled as a stochastic nonlinear impulsive differential system. The goal is to propose a method for designing a target filter that ensures the stochastic asymptotic stability of the filtering error system and guarantees a prescribed L2‐L∞ performance. Based on a time‐varying Lyapunov functional, by virtue of a convex combination technique, a design method to achieve such a filter is formulated in the form of solving a set of linear matrix inequalities. The effectiveness of the proposed filtering strategy is shown via a numerical example of a stochastic Chua's circuit system.