Title :
Filtering of Markovian Jump Delay Systems Based on a New Performance Index
Author :
Baoyong Zhang ; Wei Xing Zheng ; Shengyuan Xu
Author_Institution :
Sch. of Autom., Nanjing Univ. of Sci. & Technol., Nanjing, China
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.
Keywords :
H∞ filters; Lyapunov methods; Markov processes; continuous time systems; delay systems; filtering theory; linear matrix inequalities; linear systems; passive filters; stability; stochastic systems; time-varying systems; H∞ filtering problems; L2-L∞ passive filtering problems; MJSs; Markovian jump delay systems; continuous-time linear Markovian jump systems; delay-dependent conditions; dissipative filtering problems; extended dissipative inequality; filtering error system; linear matrix inequalities; mode-dependent Lyapunov-Krasovskii functional; mode-dependent filter design; mode-independent filter design; new performance index; stochastic stability analysis; time-varying delay system; weighting matrices; Circuit stability; Delays; Linear matrix inequalities; Performance analysis; Stability criteria; Time-varying systems; Extended dissipativity; Markovian jump systems; mode-dependent filters; mode-independent filters; time-varying delays;
Journal_Title :
Circuits and Systems I: Regular Papers, IEEE Transactions on
DOI :
10.1109/TCSI.2013.2246213