Analysis of linear asynchronous hybrid stochastic systems and its application to multi-agent systems with Markovian switching topologies

ABSTRACT

This paper studies the stability and stabilisation of a class of asynchronous hybrid stochastic systems described by linear Markov jump systems with asynchronous parameters induced by hysteretic mode and input delay. By exploring the essential properties of the Markov chain and developing novel Lyapunov function/functional based approaches, we derive sufficient conditions in terms of sizes of the delays ensuring the mean square asymptotical stability of the systems. Interestingly, the Lyapunov functional based approach further leads to the mean square stability criteria that depend only on the drift part and allow an arbitrary large delay for the diffusion part, which is different from the Lyapunov-Razumikhin based results. The theoretical results are applied to solve the consensus problems of multi-agent systems with Markovian switching topologies and input delay. Numerical examples demonstrate the established results.

KEYWORDS:

• Hybrid stochastic systems
• asynchronous switching
• time delay
• Markovian jump
• mean square stability

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 https://yalmip.github.io/

2 https://www.mosek.com/

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China under Grants 61733008, 61573156, 61873099, 61803108, and in part by the Scholarship from China Scholarship Council under Grant 201806150120.

Notes on contributors

Shixian Luo

Shixian Luo received the B.S. and M.S. degrees in Applied Mathematics, both from Guangxi University, Nanning, China, in 2013 and 2016, respectively. Now he is pursuing the Ph.D. degree at School of Automation Science and Engineering, South China University of Technology. He is now also a visiting research student in the School of Engineering, RMIT University, Australia. His current research interests include stability and control of stochastic hybrid systems, networked control systems, and event-triggered control.

Feiqi Deng

Feiqi Deng received the Ph.D. degree in control theory and control engineering from South China University of Technology, Guangzhou, in June 1997. Since October 1999, he has been a professor with South China University of Technology and the director of the Systems Engineering Institute of the university. He is currently a member of Technical Committee on Control Theory (TCCT), Chinese Association of Automation, and now he is serving as the chairs of the IEEE CSS Guangzhou Chapter and IEEE SMC Guangzhou Chapter, a vice editor-in-chief of Journal of South China University of Technology, and a member of the editorial boards of the following journals: IEEE Access, Control Theory and Applications, All about Systems and Control, Journal of Systems Engineering and Electronics, Journal of Systems Engineering, etc. His main research interests include stability, stabilisation, and robust control theory of complex systems, including time-delay systems, nonlinear systems and stochastic systems. He has published over three hundreds of journal papers on IEEE Transactions on Automatic Control, Automatica, SIAM Journal of Control and Optimization, International Journal of Systems Science and Systems & Control Letters, etc.

Xueyan Zhao

Xueyan Zhao is an associate professor of School of Automation Science and Engineering, South China University of Technology. She received the Ph.D degree in Systems Engineering from South China University of Technology, Guangzhou, in June 2014. Her research interests are stability and stabilisation of stochastic systems and nonlinear systems. In recent years, she published more than 20 papers indexed by SCI in IEEE Transactions on Automatic Control, Automatica, SIAM Journal on Control and Optimization and so on.