Stability analysis for stochastic nonlinear systems with state-dependent switching and time-delay

Abstract

The stability of stochastic nonlinear systems with time-delay and state-dependent switching is studied in this paper. Firstly, system maximal solution is constructed and further extended as the global solution under certain mild conditions. Secondly, several Krasovskii-type stability and Razumikhin-type theorems are proposed by uniformly asymptotically stable functions (UASFs). These stability criteria overcome some stringent constraints associated with Lyapunov functional/functions. Finally, the theoretical findings are validated through two simulation examples.

Keywords:

• Stochastic nonlinear systems
• time delay
• state-dependent switching
• uniformly asymptotically stable function

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by National Natural Science Foundation of China [62073275] and Shandong Provincial Natural Science Foundation of China [ZR2020MA033].