L₂-L_∞ filtering for a class of stochastic nonlinear systems with aperiodic sampling

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.