H ∞ estimation for discrete-time piecewise homogeneous Markov jump linear systems

• Published in: Automatica (Oxford) Vol. 45; no. 11; pp. 2570 - 2576
• Main Author: Zhang, Lixian
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.11.2009; Elsevier
• Subjects: [formula omitted] filtering; Applied sciences; Arbitrary variation and stochastic variation of TP matrices; Computer science; control theory; systems; Control theory. Systems; Exact sciences and technology; Markov jump linear systems; Modelling and identification; Piecewise homogeneous TPs; Markov jump linear systems; Piecewise homogeneous TPs; H ∞ filtering; Arbitrary variation and stochastic variation of TP matrices; Markov process; Probabilistic approach; H infinite control; H; Linear time; ofTP matrices; Closed feedback; Transition matrix; Time varying system; Time domain method; Filter; Discrete time; Transition probability; Jump process; Jumping; filtering; Piecewise linearization; Arbitrary variation and stochastic variation
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2009.07.004

This paper concerns the problem of H ∞ estimation for a class of Markov jump linear systems (MJLS) with time-varying transition probabilities (TPs) in discrete-time domain. The time-varying character of TPs is considered to be finite piecewise homogeneous and the variations in the finite set are considered to be of two types: arbitrary variation and stochastic variation, respectively. The latter means that the variation is subject to a higher-level transition probability matrix. The mode-dependent and variation-dependent H ∞ filter is designed such that the resulting closed-loop systems are stochastically stable and have a guaranteed H ∞ filtering error performance index. Using the idea in the recent studies of partially unknown TPs for the traditional MJLS with homogeneous TPs, a generalized framework covering the two kinds of variations is proposed. A numerical example is presented to illustrate the effectiveness and potential of the developed theoretical results.