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Stability

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Analysis and Design of Singular Markovian Jump Systems

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Abstract

Stability problem is essential and important in control theory and dynamic system analysis. In this chapter, the fundamental problem of stability for SMJSs with general TRMs is considered, in which the TRMs may be exactly known, uncertain, partially unknown and designed. The conditions guaranteeing a given SMJS stochastically admissible are expressed in terms of LMIs or LMIs with equation constraints which can be efficiently solved by using the standard numerical algorithms. Specifically, when TRM is given precisely, necessary and sufficient conditions in different forms are developed. Then, the robust stability of Markovian jump singularly perturbed systems with uncertain switchings and nonlinear perturbations for any perturbation parameter \(\varepsilon \in (0,\bar{\varepsilon }]\) is solved by an LMI approach. Moreover, instead of just containing \(\varepsilon \), a set of conditions guaranteeing the existence and uniqueness of a solution, as well as stochastic admissibility, is established by choosing an \(\varepsilon \)-dependent Lyapunov function and only depends on stability bound. It is worth mentioning that the stability results proposed in this chapter will play important roles in dealing with other problems discussed in this book.

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Author information

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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Corresponding author

Correspondence to Guoliang Wang .

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© 2015 Springer International Publishing Switzerland

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Wang, G., Zhang, Q., Yan, X. (2015). Stability. In: Analysis and Design of Singular Markovian Jump Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-08723-8_2

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  • DOI: https://doi.org/10.1007/978-3-319-08723-8_2

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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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