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Robust H 2 Filtering for Discrete‐Time Markovian Jump Linear Systems
Author(s) -
Liu Tao,
Zhang Hao,
Chen Qijun
Publication year - 2012
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.470
Subject(s) - control theory (sociology) , mathematics , filter (signal processing) , norm (philosophy) , filtering problem , filter design , linear matrix inequality , upper and lower bounds , linear system , jump , markov process , matrix (chemical analysis) , mathematical optimization , computer science , statistics , mathematical analysis , physics , materials science , control (management) , quantum mechanics , artificial intelligence , political science , law , composite material , computer vision
This paper studies the problems of H 2 filtering for discrete‐time M arkovian jump linear systems with non‐accessible mode information. The objective is to design a less‐conservative mode‐independent H 2 filter such that the filtering error system is stochastically stable. To this end, sufficient conditions for the existence of an upper bound of H 2 norm are given in terms of linear matrix inequalities. With the introduction of a slack variable, a less‐conservative filter is derived. The proposed robust H 2 filter design method is also applicable to cover the cases where the system matrices are subject to polytopic uncertainty, as well as the case where the transition probability matrix is subject to a given polytopic uncertainty. Application of the proposed method to three examples from the literature demonstrates the favorable performance of the proposed solution to existing approaches.