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

Authors:
Lixian Zhang
Affiliations:
Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin 150001, China
Venue:
Automatica (Journal of IFAC)
Year:
2009

Citing 2
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Abstract

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.