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L 1 control for positive Markovian jump systems with partly known transition rates

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  • Control Theory and Applications
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Abstract

This paper deals with the problem of L 1 control for positive Markovian jump systems with partly known transition rates. First, by constructing an appropriate linear co-positive type Lyapunov-Krasovskii function, stochastic stability for the underlying system is discussed. Then, the L 1-gain performance is analyzed. Based on the results obtained, an effective method is proposed for the design of state feedback controller. All the proposed conditions are derived to ensure that the closed-loop Markovian jump system positive and stochastically stable with L 1-gain performance in linear programming. Finally, an example is given to demonstrate the validity of the main results.

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Authors and Affiliations

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

    Wenhai Qi & Xianwen Gao

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  1. Wenhai Qi
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  2. Xianwen Gao
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Correspondence to Wenhai Qi.

Additional information

Recommended by Associate Editor Juhoon Back under the direction of Editor Yoshito Ohta. This work is supported by Key Program of National Natural Science Foundation of China (61573088) and (61433004).

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. Now, he is a Ph.D. candidate in Northeastern University,Shenyang, P.R. China. His research work focus on Markovian jump systems, positive systems, etc.

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., Gao, X. L 1 control for positive Markovian jump systems with partly known transition rates. Int. J. Control Autom. Syst. 15, 274–280 (2017). https://doi.org/10.1007/s12555-014-0444-2

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  • DOI: https://doi.org/10.1007/s12555-014-0444-2

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