Abstract
This paper is concerned with stochastic admissibility and state feedback stabilization for a class of singular Markovian jump systems with multiple time-varying delays. The singular matrix E with both modedependent and mode-independent is considered in the system. Firstly, based on Lyapunov functional method and free-weighting matrix method, sufficient condition is presented in the form of linear matrix inequalities (LMIs) to guarantee the considered system to be stochastically admissible. Secondly, by state feedback controller, sufficient condition is derived in terms of strict LMIs to ensure the closed-loop system to be stochastically stabilizable. Finally, numerical examples are provided to illustrate the effectiveness of the proposed approaches.
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Recommended by Associate Editor Sung Jin Yoo under the direction of Editor PooGyeon Park. This work is supported by the National Natural Science Foundations of China(61473097).
Baoping Jiang received his M.S. degree in operational research and cybernetics from Ocean University of China in 2015. Now, he is a Ph.D. candidate in Marine mathematical at Ocean University of China. His research interests include singular systems, Markovian jumping systems, stability theory and so on.
Cunchen Gao received his Ph.D degree from South China University of Technology. He is presently a full professor at School of Mathematical Sciences, Ocean University of China. His research interests include variable structure control, distributed parameter systems, time-delay systems, singular systems and so on.
Yonggui Kao 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 jumping systems, artificial intelligence, neural networks, stability theory and sliding mode control.
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Jiang, B., Gao, C. & Kao, Y. Stochastic admissibility and stabilization of singular Markovian jump systems with multiple time-varying delays. Int. J. Control Autom. Syst. 14, 1280–1288 (2016). https://doi.org/10.1007/s12555-015-0180-2
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DOI: https://doi.org/10.1007/s12555-015-0180-2