Filtering of Markovian jump delay systems based on a new performance index

Baoyong Zhang, Wei Xing Zheng, Shengyuan Xu

    Research output: Contribution to journalArticlepeer-review

    447 Citations (Scopus)

    Abstract

    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.
    Original languageEnglish
    Pages (from-to)1250-1263
    Number of pages14
    JournalIEEE Transactions on Circuits and Systems I: Regular Papers
    Volume60
    Issue number5
    DOIs
    Publication statusPublished - 2013

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