Filtering of Markovian Jump Delay Systems Based on a New Performance Index

This paper is concerned with the design of mode-dependent and mode-independent filters for continuous-time linear Markovian jump systems (MJSs) with time-varying delays. Different from the existing studies in the literature, the purpose of this paper is to solve the H_∞, L₂ - L_∞ passive and dissipative filtering problems in a unified framework. This purpose is successfully realized by using a new performance index that is referred to as extended dissipativity. The extended dissipative inequality contains several weighting matrices. By tuning the weighting matrices, the extended dissipativity will reduce to the H_∞ performance, L₂ - L_∞ performance, passivity and dissipativity, respectively. Delay-dependent conditions for the analysis of stochastic stability and extended dissipativity for MJSs with time-varying delays are obtained by using a mode-dependent Lyapunov-Krasovskii functional together with a novel integral inequality. Based on these conditions, the design methods for mode-dependent and mode-independent filters are developed based on linear matrix inequalities. The designed filters guarantee that the resulting filtering error system is stochastically stable and extended dissipative for any admissible delays. Finally, the effectiveness of the proposed methods is substantiated with three illustrative examples.