\(H_{\infty }\) Model Reduction

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


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.


Stochastic Variation TPMTransition Probability Matrix Arbitrary Variation Jump Linear System Real Lemma 
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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Lixian Zhang
    • 1
    Email author
  • 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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