Finite-time input-to-state stability of discrete-time stochastic switched systems: a comparison principle-based method

Abstract

This paper studies the input-to-state stability (ISS) and the finite-time input-to-state stability issues for the discrete-time stochastic switched nonlinear systems with time-varying delay. Based on the improved vector-version comparison principle and by employing the stochastic analysis method, sufficient conditions are first derived to guarantee the discrete-time stochastic switched system to be finite-time input-to-state stable in mean and finite-time stochastic input-to-state stable. Then, the comparison principle is further utilised to establish the p-th moment ISS result. As an application, the mean-square ISS is analysed for the linear discrete-time stochastic switched system. At the end of the paper, two numerical examples are provided to illustrate the feasibility/effectiveness of the obtained results.

Keywords:

• Finite-time input-to-state stability
• finite-time stochastic input-to-state stability
• comparison principle
• stochastic switched system

Disclosure statement

No potential conflict of interest was reported by the authors.

Data availability statement

Data sharing is not applicable to this article as it describes entirely theoretical research.

Additional information

Funding

This work was supported in part by the National Key Research and Development Program of China [grant number 2018AAA0100202], in part by the National Natural Science Foundation of China [grant number  61877033], in part by the Natural Science Foundation of Shandong Province [grant number  ZR2019MF021], in part by the Development Plan of Youth Innovation Team in Universities of Shandong Province,  and in part by the Key Project of Natural Science Foundation of China [grant number 61833005].

Notes on contributors

Shuang Liang

Shuang Liang received the B.Sc. degree in Statistics from Shandong University, Jinan, China, in 2011, and the M.Sc. degree in Systems Theory from Harbin Engineering University, Harbin, China, in 2015. Since 2016, she is pursuing the Ph.D. degree from Southeast University, Nanjing, China. Her current research interests include stochastic systems, stability theory, etc.

Jinling Liang

Jinling Liang received the B.Sc. and M.Sc. degrees in Mathematics from Northwest University, Xi'an, China, in 1997 and 1999, respectively, and the Ph.D. degree in Applied Mathematics from Southeast University, Nanjing, China, in 2006. She is currently a Professor in the School of Mathematics, Southeast University. She has published around 90 papers in refereed international journals. Her current research interests include neural networks, complex networks, and two-dimensional systems.

Jianlong Qiu

Jianlong Qiu received the M.Sc. and Ph.D. degrees in Applied Mathematics from Southeast University, Nanjing, China, in 2000 and 2007, respectively. From 2009 to 2010, he was a Visiting Scholar at Stevens Institute of Technology, Hoboken, NJ, USA. From 2014 to 2015, he was a Visiting Scholar at University of Rhode Island, South Kingstown, RI, USA. He is currently a Professor in the School of Automation and Electrical Engineering, Linyi University. He has published around 100 papers in a referred international journal. His current research interests include computational intelligence, stability theory in neural networks and complex networks.