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Composite TPs Case

  • 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 is concerned with the robust stability problem for a class of discrete-time uncertain Markov jump systems (MJSs) with both partially unknown and uncertain transition probabilities (TPs). Therefore, the scenario is more practical and such TPs comprise three sorts: known, uncertain and unknown. Moreover, the system considered in this chapter is specifically meant to be a class of Markov jump neural networks (MJNNs) with uncertainties and perturbations. The parameters uncertainties are considered to be norm-bounded and the stochastic perturbations are described in forms of the Brownian motion. By invoking the property of the transition probabilities matrix (TPM) and the convexity of uncertain domains, a sufficient stability criterion for the underlying system is derived. Furthermore, a monotonicity is observed in concern of the maximum value of a given scalar which bounds the stochastic perturbation that the system can tolerate as the level of the defectiveness varies.

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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