Asynchronous Filtering for Delayed Fuzzy Jump Systems Subject to Mixed Passivity and ${\\user2{H\\infty }} $ Performance

Abstract

This paper investigates asynchronous mixed passivity and $$H\\infty $$\n filter design for fuzzy jump systems with time-varying delays. Firstly, new time delay-dependent stability conditions for the fuzzy Markovian jump systems are obtained by constructing a mode-dependent Lyapunov functional and introducing free weight matrices technique. Secondly, the asynchronous filter is designed via linear matrix inequalities, which can ensure stochastic stability and the mixed passivity and $$H\\infty $$\n performance of the augmented Markovian jump filtering error system. A numerical example and a single-link robot arm are utilized to show the effectiveness of the method.