Stabilisation of stochastic coupled systems via feedback control based on discrete-time state observations

ABSTRACT

This paper is concerned with the stabilisation of stochastic coupled systems (SCSs) via feedback control based on discrete-time state observations. State feedback control based on discrete-time observations is designed in the drift parts of the SCSs. Based on graph theory and Lyapunov method, the upper bound of the duration between two consecutive state observations is obtained. And a systematic method is given to construct a global Lyapunov function for SCSs via feedback control based on discrete-time state observations. A Lyapunov-type theorem and a coefficient-type criterion are obtained to guarantee the stabilisation in the sense of mean-square asymptotical stability and mean-square exponential stability. Furthermore, we use the theoretical results to analyse the stabilisation of stochastic coupled oscillators. Finally, we give a numerical example to illustrate the effectiveness and feasibility of the developed theoretical results.

KEYWORDS:

• Exponentially stable
• stabilisation
• stochastic coupled systems
• discrete-time state
• feedback control

Acknowledgments

The authors really appreciate the reviewers’ valuable comments. This work was supported by the NNSF of China (Nos. 11301112 and 11401136), the Educational Commission of Guangdong Province, China (2014KTSCX113), the NSF of Shandong Province (Nos. ZR2013AQ003 and ZR2014AQ010), China Postdoctoral Science Foundation funded project (No. 2014T70313) and HIT. IBRSEM. A. 2014014.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

NNSF of China [grant number 1301112], [grant number 11401136]; Educational Commission of Guangdong Province, China [grant number 2014KTSCX113]; NSF of Shandong Province [grant number ZR2013AQ003], [grant number ZR2014AQ010]; China Postdoctoral Science Foundation [grant number 2014T70313].

Notes on contributors

Yongbao Wu

Yongbao Wu was born in 1992. He is currently a M.S. student in Harbin Institute of Technology, China. His current research interests include stability theory for stochastic differential equations and stochastic control theory here.

Wenxue Li

Wenxue Li was born in 1981. He received his Ph.D. degree from Harbin Institute of Technology, China, in 2009. He is currently an associate professor in Harbin Institute of Technology at Weihai. His current research interests include stability theory for stochastic differential and integral equations.

Jiqiang Feng

Jiqiang Feng received the B.Sc. degree from Yantai Normal College in 2005, M.Sc. and Ph.D. degrees from Shenzhen University in 2008 and 2011, respectively. He joined the Shenzhen University, Shenzhen, China in 2011 and currently is a lecturer. His research interests are swarm optimization, neural network theory and optimization.