Stability Probabilities of Sliding Mode Control of Linear Continuous Markovian Jump Systems

  • Jiaming ZhuEmail author
  • Xinghuo Yu


In this chapter, an equivalent control-based sliding mode control is proposed for linear Markovian jump systems, which guarantees the asymptotical stability. The control objects are single-input single-output systems and multi-input multi-output systems. By using the stochastic system theory, a multi-step state transition conditional probability function is introduced for the continuous Markovian process, which is used to define the reaching and sliding probabilities. Furthermore, the formulas for calculating reaching and sliding probabilities are derived for situations where the control force may not be strong enough to ensure the fully asymptotical stability. In particular, for multi-input multi-output systems, by using the linear matrix inequality approach, sufficient conditions are proposed to guarantee the stochastically asymptotical stability of the systems on the sliding surfaces. Extensive simulations are conducted to validate the theoretical results and show the relationship between the control force and reaching and sliding probabilities.



The authors would like to thank the editor and the reviewers for their helpful and valuable comments and suggestions, which have improved the presentation. This work is supported by National Natural Science Foundation of China under Grant no’s. 61573307, 61273352, 61473249, 61473250, 61175111, 61174046, and the Australian Research Council (No. DP140100544.)


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Yangzhou UniversityYangzhouChina
  2. 2.RMIT UniversityMelbourneAustralia

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