Mixed dissipative filtering design for uncertain singular Markovian jump time-varying delay systems with nonlinear perturbations and generally uncertain transition rates

Abstract

This paper studies the dissipative filtering of uncertain singular time-varying delay Markovian jump systems (MJSs) with nonlinear perturbations and generally uncertain transition rates (GUTRs). We focus on the design of a mixed filter, which can include mode-dependent and mode-independent filters in a unified and simple structure. First, a new Lyapunov–Krasovskii functional is proposed through the delay-decomposition approach, and improved Wirtinger-based integral inequalities are used to obtain a sufficient condition to ensure the stochastic admissibility of the considered uncertain nonlinear singular time-varying delay MJSs with dissipative performance. Based on these ingredients, the explicit expression of the desired mixed filter is obtained. Finally, some numerical examples and the filter design of a two-loop circuit network reflect the less conservatism and effectiveness of the method in this article.