H∞ model reduction

Lixian Zhang; Ting Yang; Peng Shi; Yanzheng Zhu

doi:10.1007/978-3-319-28847-5_8

H_∞ model reduction

Lixian Zhang^*
, Ting Yang
, Peng Shi
, Yanzheng Zhu

^*Corresponding author for this work

School of Astronautics, Harbin Institute of Technology
Adelaide University
Victoria University

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

This chapter concerns the problem of model reduction for a class of Markov jump linear system (MJLS) with time-varying (or nonhomogeneous) transition probabilities (TPs) in discrete-time domain. The time-varying character of TPs is considered as finite piecewise homogeneous and the variations in the finite set are considered as two types: arbitrary variation and stochastic variation, respectively. The latter means that the variation is subject to a higher-level transition probability matrix (TPM). Invoking 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 variation is proposed. The model reduction results for the underlying systems are obtained in H_∞ sense. A numerical example is presented to illustrate the effectiveness and potential of the developed theoretical results.

Original language	English
Title of host publication	Studies in Systems, Decision and Control
Publisher	Springer International Publishing
Pages	173-185
Number of pages	13
DOIs	https://doi.org/10.1007/978-3-319-28847-5_8
State	Published - 2016
Externally published	Yes

Publication series

Name	Studies in Systems, Decision and Control
Volume	54
ISSN (Print)	2198-4182
ISSN (Electronic)	2198-4190

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10.1007/978-3-319-28847-5_8

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AU - Shi, Peng

AU - Zhu, Yanzheng

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AB - This chapter concerns the problem of model reduction for a class of Markov jump linear system (MJLS) with time-varying (or nonhomogeneous) transition probabilities (TPs) in discrete-time domain. The time-varying character of TPs is considered as finite piecewise homogeneous and the variations in the finite set are considered as two types: arbitrary variation and stochastic variation, respectively. The latter means that the variation is subject to a higher-level transition probability matrix (TPM). Invoking 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 variation is proposed. The model reduction results for the underlying systems are obtained in H∞ sense. A numerical example is presented to illustrate the effectiveness and potential of the developed theoretical results.

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H_∞ model reduction

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