Abstract
The paper is concerned with positive observer design for positive Markovian jump systems with incomplete transition rates and time delays that are mode-dependent and time-varying. Firstly, by applying an appropriate co-positive type Lyapunov-Krasovskii function and free-connection weighting vectors, sufficient conditions are proposed to ensure stochastic stability of the error positive system and existence of the positive observer. All the proposed conditions are derived in linear programming. Finally, an example is given to demonstrate the validity of the main results.
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Recommended by Associate Editor M. Chadli under the direction of Editor Myo Taeg Lim. This work was supported by Key Program of National Natural Science Foundation of China under Grant No. 61573088 and 61433004.
Jiyang Wang was born in Shenyang, Liaoning Province, P. R. China, in 1986.He received his B.S. degree from Northeastern University in 2008 and his M.S.degree from The University of Sheffield (UK) in 2011. He is currently a Ph.D. student in Northeastern University. His main research interests are modeling of complex industry process and intelligent control, stochastic jump systems, etc.
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.
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 jumping systems, artificial intelligence, neural networks, stability theory and sliding mode control.
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Wang, J., Qi, W., Gao, X. et al. Positive observer design for positive Markovian jump systems with mode-dependent time-varying delays and incomplete transition rates. Int. J. Control Autom. Syst. 15, 640–646 (2017). https://doi.org/10.1007/s12555-015-0297-3
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DOI: https://doi.org/10.1007/s12555-015-0297-3