Stabilisation and H_∞ control of neutral stochastic delay Markovian jump systems

ABSTRACT

This paper investigates the exponential stabilisation and H_∞ control problem of neutral stochastic delay Markovian jump systems. First, a delay feedback controller is designed to stabilise the neutral stochastic delay Markovian jump system in the drift part. Second, sufficient conditions for the existence of feedback controller are proposed to ensure that the resulting closed-loop system is exponentially stable in mean square and satisfies a prescribed H_∞ performance level. Finally, numerical examples are provided to show the effectiveness of the proposed design methods.

KEYWORDS:

• Stabilisation
• H_∞ control
• neutral stochastic delay Markovian jump system
• stability

Ackowledgments

The authors would like to thank the editor and referees for their very helpful comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

National Natural Science Foundation of China [grant number 61573007], [grant number 61403199], [grant number 61673218], [grant number 61374153], [grant number 61473151].

Notes on contributors

Weimin Chen

Weimin Chenreceived his B.Sc. degree from Anhui Normal University, China in 2000, M.Sc. degree and Ph.D. degree from Nanjing University of Science and Technology, China in 2003 and 2014, respectively. He now is an Associate Professor at School of Science, Nanjing University of Science and Technology. His current research interests include stochastic systems, Markovian jumping systems, neural networks, stability theory and control.

Qian Ma

Qian Ma received the B.Sc. degree in computational mathematics from Jiangsu University of Science and Technology, in 2005, the M.Sc. degree in fluid dynamics from Nanjing University of Science and Technology, in 2007 and Ph. D degree in control theory from Nanjing University of Science and Technology, in 2013. Since June 2013, she has joined the School of Automation at Nanjing University of Science and Technology, where she is currently a Professor. Her current research interests include time-delay systems, stability theory and Multi-agent systems.

Lanning Wang

Lanning Wangreceived the B.E. and M.E. degrees in applied mathematics and the Ph.D. degree in control science and engineering from Nanjing University of Science and Technology, China, in 2003, 2005 and 2016, respectively. Since 2005, she has been with the School of Science, Nanjing University of Posts and Telecommunications, Nanjing, China, where she is currently an Associate Professor. Her areas of interest include multi-dimensional systems, singular systems, fuzzy systems, etc.

Huiling Xu

Huiling Xu received her B.Sc. degree in mathematics from the Nanjing University of Science and Technology, China in 1992, and the M.S. and Ph.D. degrees in control science and control engineering from the Nanjing University of Science and Technology, China in 1999 and 2005, respectively. From 2009 to 2011 she was a Research Fellow in the school of electrical and electronic engineering at the Nanyang Technological University (NTU), Singapore. Since Apr. 2012, she has been a Professor in the school of science at the Nanjing University of Science and Technology, China. Her current research interests include distributed control, multidimensional systems, singular systems, time-delay systems, modeling and optimization for big data analytics.