Global asymptotic stability analysis of discrete-time stochastic coupled systems with time-varying delay

Abstract

This paper is concerned with the problem of global asymptotic stability for the discrete-time stochastic coupled systems with time-varying delay (DSCSTD). Based on graph theory and Lyapunov method, a systematic method is given for constructing a global Lyapunov function for the DSCSTD. Some novel stability criteria for the DSCSTD are obtained. Furthermore, to demonstrate the significance in practice, the theoretical results are applied to stochastic coupled oscillators. Finally, a numerical example is given to illustrate the effectiveness of the theoretical results. The above work will provide a theoretical principle for subsequent controller design of the DSCSTD in future.

Keywords:

• Discrete-time stochastic coupled systems
• time-varying delay
• global asymptotic stability
• graph theory
• lyapunov method

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Natural Science Foundation of Shandong Province of China [ZR2019MF030, ZR2018PEE018] and China Postdoctoral Science foundation [2018M641830] and the Fundamental Research Funds for the Central Universities of China [HIT.NSRIF201721] and the National Natural Science Foundation of China [61773137].