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Stability and Stabilization for Discrete-time Markovian Jump Stochastic Systems with Piecewise Homogeneous Transition Probabilities

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  • Control Theory and Applications
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Abstract

In this paper, the stability and stabilization problems for discrete-time Markovian jump stochastic systems with time-varying transition probabilities are investigated. The time-varying character of the transition probabilities is considered to be finite piecewise homogeneous and the variations in the finite set are considered to be a stochastic variation. First, a stability criterion is derived to guarantee the stochastic stability of the considered piecewise homogeneous Markovian jump stochastic system. Further, a sufficient condition on the existence of a mode-dependent state feedback controller is proposed such that the resulting closed-loop system is stochastically stable. In addition, the stability and stabilization problems are studied for the piecewise homogeneous Markovian jump stochastic system with incomplete transition descriptions. Finally, some simulation results are given to show the validity and potential of the developed results.

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Authors and Affiliations

  1. School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology, Shanghai, 200093, China

    Meijiao Zhou

  2. Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin, 150001, China

    Yanming Fu

Authors
  1. Meijiao Zhou
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  2. Yanming Fu
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Corresponding author

Correspondence to Yanming Fu.

Additional information

Recommended by Associate Editor Ohmin Kwon under the direction of Editor Jessi (Ju H.) Park. This work was supported by Maker Fund for the Individual Maker Project of Shenzhen under Grant No.GRCK2017082216484742, by the National Natural Science Foundation of China Under Grant No.61104059, and by the Natural Science Foundation of Shanghai under grant No. 17ZR1443500.

Meijiao Zhou received her Ph.D. degree in Thermal Engineering from University of Shanghai For Science and Technology in 2008. Her research interests include intelligent control and Fieldbus control.

Yanming Fu was born in 1978. He received the Ph.D. degree in Control Theory and Application from Harbin Institute of Technology, China, in 2006. Now he is currently an associate professor at the School of Astronautics, Harbin Institute of Technology. His main research interests are intelligent control, robust control and satellite attitude and orbit control.

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Zhou, M., Fu, Y. Stability and Stabilization for Discrete-time Markovian Jump Stochastic Systems with Piecewise Homogeneous Transition Probabilities. Int. J. Control Autom. Syst. 17, 2165–2173 (2019). https://doi.org/10.1007/s12555-018-0490-2

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  • DOI: https://doi.org/10.1007/s12555-018-0490-2

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