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\(H_{\infty }\) Model Reduction

  • Lixian Zhang
  • Ting Yang
  • Peng Shi
  • Yanzheng Zhu
Chapter
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 54)

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 \(H_{\infty }\) sense. A numerical example is presented to illustrate the effectiveness and potential of the developed theoretical results.

Keywords

Stochastic Variation TPMTransition Probability Matrix Arbitrary Variation Jump Linear System Real Lemma 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Lixian Zhang
    • 1
  • Ting Yang
    • 1
  • Peng Shi
    • 2
    • 3
  • Yanzheng Zhu
    • 1
  1. 1.School of AstronauticsHarbin Institute of TechnologyHarbinChina
  2. 2.School of Electrical and Electronic EngineeringThe University of AdelaideAdelaideAustralia
  3. 3.College of Engineering and ScienceVictoria UniversityMelbourneAustralia

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