<i>L₂-L_∞</i> filtering for stochastic delayed systems with randomly occurring nonlinearities and sensor saturation

Abstract

This work investigates L2-L∞ filtering problem for a class of stochastic systems with time-delay and randomly occurring phenomena. The purpose of the addressed problem is to design a full order filter to ensure the filtering error system is asymptotically mean-square stable with prescribed L2-L∞ performance. A novel stochastic time-delay system model is established, in which randomly occurring nonlinearities and sensor saturation phenomena are considered. Then, a novel functional containing negative definite terms is constructed to relax the constraints on the functional, and a new free-matrix-based stochastic integral inequality is also given. Meanwhile, a novel L2-L∞ performance analysis method making full use of delay information is proposed. As a result, less conservative conditions for the existence of filters are obtained, under which the L2-L∞ performance level can be achieved for the filtering error system. Numerical examples are employed to show the benefits of the proposed approach.