Stability and stabilisation of Itô stochastic systems with piecewise homogeneous Markov jumps

ABSTRACT

This paper focuses on the problem of stability and stabilisation for continuous-time Itô stochastic Markovian jump linear systems with time-varying transition rates. The time-varying property of the transition rates is considered to be finite piecewise homogeneous. Firstly, the stability conditions of the piecewise homogeneous Itô stochastic Markovian jump linear systems are given in terms of linear matrix inequalities (LMIs). Especially, a novel stability criterion is developed for the considered systems by the existence of the unique positive-definite solution of the corresponding coupled Lyapunov matrix equations. Secondly, two state-feedback controllers are designed via LMIs to stabilise the systems. Finally, a practical example is provided to illustrate the effectiveness of the presented theoretical results.

Keywords:

• Markovian jump systems
• time-varying transition rates
• stability analysis
• state-feedback control

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Shenzhen Municipal Basic Research Project for Discipline Layout with project no. JCYJ20170413112722597, by the National Natural Science Foundation of China under grant nos. 61603111 and 61333003, by the Major Program of National Natural Science Foundation of China under grant nos. 61690210 and 61690212, by Shenzhen Municipal Project for Basic Research with project nos. JCYJ20170307150952660 and JCYJ20170307150227897.

Notes on contributors

Hui-Jie Sun

Hui-Jie Sun was born in Inner Mo, P.R. China on 2 August 1988. He received the BEng degree in Automation in July 2011 from Harbin Institute of Technology, MEng degree in January 2014 and Ph.D degree in September 2018 all in Control Science and Engineering from Harbin Institute of Technology, Shenzhen. He is currently a post-doctoral researcher in Harbin Institute of Technology, Shenzhen. His research interest covers system identification, stochastic systems, and iterative algorithms.

Ai-Guo Wu

Ai-Guo Wu was born in Gong'an County, Hubei Province, P. R. China on 20 September 1980. He received his B.Eng degree in Automation in July 2002, M.Eng degree in Navigation, Guidance and Control in July 2004 and Ph.D degree in Control Science and Engineering in Nov. 2008 all from Harbin Institute of Technology. In Oct. 2008, he joined Harbin Institute of Technology Shenzhen Graduate School as an assistant professor, and in August 2012 he was promoted to a professor. From Jan. 2018, he is a professor in Harbin Institute of Technology, Shenzhen. Dr. Wu was a Research Fellow with the Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong from March 2009 to March 2011. He was a visiting professor with the Department of Electrical, Electronic and Computer Engineering of The University of Western Australia, Australia from July 2013 to July 2014. His research interests include descriptor systems, conjugate product of polynomials, switched system and robust control. He has authored/coauthored one English monograph and more than 60 SCI journal papers. He received the National Natural Science Award (Second Prize) in 2015 from P.R. China, and the National Excellent Doctoral Dissertation Award in 2011 from the Academic Degrees Committee of the State Council and the Ministry of Education of P.R. China. He was supported by the Program for New Century Excellent Talents in University in 2011, and by the National Natural Science Foundation of China for Excellent Young Scholars in 2018. Dr. Wu is a Reviewer for American Mathematical Review from 2007. He serves as a Regional Editor of Nonlinear Dynamics and Systems Theory from 2015, and an International Subject Editor of Applied Mathematical Modelling from 2017. He was an Outstanding Reviewer for IEEE Transactions on Automatic Control in 2010.

Ying Zhang

Ying Zhang was born in Jilin Province. She received her MEng. degree in Control Theory and Control Engineering from Harbin University of Science and Technology in 2003 and Ph.D. degree in Control Science and Engineering in 2007 from Harbin Institute of Technology. From 2007 to 2010, she was a post-doctoral researcher in Harbin Institute of Technology Shenzhen Graduate School, where she became an assistant professor in 2010 and associate professor in 2011. She is now an associate professor in Harbin Institute of Technology, Shenzhen. Her main research interests include robust control and filter theory, networked control systems. She is the corresponding author of this paper.