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Applications of a Markov Process

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Analysis and Design of Singular Markovian Jump Systems

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Abstract

This chapter studies the applications of a Markov process on deterministic singular systems whose parameters are only with one mode. The first application is on an uncertain singular system which has norm bounded uncertainties on system matrices. According to the maximum singular value of uncertainty, the uncertainty set is separated into several different subsets. Then, the original system without jumping is transformed into an MJS, whose switching probability of subsets is considered in system analysis and synthesis. New version of BRL is developed by exploiting an uncertainty-dependent Lyapunov function. Two conditions for uncertainty-dependent controllers are established. Based on the key idea, the time-varying delay of the singular system is described by a Markov process, whose distribution property is also considered. Sufficient conditions for the solvability of delay-distribution-dependent stability with both exact known or uncertain TRMs are derived, and state feedback controllers depending on such a distribution are designed via the LMI approach.

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Authors and Affiliations

  1. Liaoning Shihua University, Fushun, China

    Guoliang Wang

  2. Institute of Systems Science, State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, China

    Qingling Zhang

  3. School of Engineering and Digital Arts, The University of Kent, Kent, CT, UK

    Xinngang Yan

Authors
  1. Guoliang Wang
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  2. Qingling Zhang
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  3. Xinngang Yan
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Correspondence to Guoliang Wang .

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© 2015 Springer International Publishing Switzerland

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Wang, G., Zhang, Q., Yan, X. (2015). Applications of a Markov Process. In: Analysis and Design of Singular Markovian Jump Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-08723-8_8

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  • DOI: https://doi.org/10.1007/978-3-319-08723-8_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08722-1

  • Online ISBN: 978-3-319-08723-8

  • eBook Packages: EngineeringEngineering (R0)

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