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Passivity and passification for stochastic systems with Markovian switching and generally uncertain transition rates

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  • Control Theory and Applications
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Abstract

The paper deals with the problems of passivity and passification for stochastic systems with Markovian switching and generally uncertain transition rates. The considered systems are more general, which cover uncertain transition rates and partly known transition rates as two special cases. By employing the multiple Lyapunov function and some free-weighting matrices, a state feedback controller is constructed such that the resulted closed-loop system is stochastically passive. Some sufficient conditions for the solution to the problem are derived in the form of linear matrix inequalities (LMIs). Finally, a numerical example is given to demonstrate the validity of the main results.

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Author information

Authors and Affiliations

  1. Department of Automation, Qufu Normal University, Rizhao, 276826, China

    Wenhai Qi

  2. College of Science, Harbin Institute of Technology, Weihai, 264200, China

    Yonggui Kao

  3. School of Information Science and Engineering, Northeastern University, Shenyang, 110819, China

    Xianwen Gao

Authors
  1. Wenhai Qi
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  2. Yonggui Kao
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Corresponding author

Correspondence to Wenhai Qi.

Additional information

Recommended by Associate Editor Yang Tang under the direction of Editor Hamid Reza Karimi. This work was supported by National Natural Science Foundation of China under Grant No. 61473097 and 61573088.

Wenhai Qi was born in Taian, Shandong Province, P. R. China, in 1986. He received his B.S. degree in automation from Qufu Normal University in 2008 and his M.S. degree from Qufu Normal University in 2013. In 2016, he received his Ph.D. degree in control theory and control engineering from Northeastern University. He now works in Qufu Normal University. His research work focuses on Markovian switching systems, positive systems, etc.

Yonggui Kao received the B.E. degree from Beijing Jiaotong University in 1996. He received his M.E. and Ph.D. degrees from Ocean University of China in 2005 and 2008, respectively. He now is an Associate Professor at Department of Mathematics, Harbin Institute of Technology (Weihai). His research interest covers stochastic systems, impulsive systems, singular systems, Markovian switching systems, artificial intelligence, neural networks, stability theory and sliding mode control.

Xianwen Gao received his B.S. degree from Shenyang University of Chemical Technology in 1978 and his M.S. degree from Northeastern University in 1993. In 1998, he received his Ph.D. degree in control theory and control engineering from Northeastern University. He is currently a professor in Northeastern University. His main research interests are modeling of complex industry process and intelligent control, stochastic jump systems, etc.

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Qi, W., Kao, Y. & Gao, X. Passivity and passification for stochastic systems with Markovian switching and generally uncertain transition rates. Int. J. Control Autom. Syst. 15, 2174–2181 (2017). https://doi.org/10.1007/s12555-016-0615-4

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  • DOI: https://doi.org/10.1007/s12555-016-0615-4

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