Stability analysis for highly nonlinear switched stochastic systems with time-varying delays

Abstract

In this paper, we examine the stability of highly nonlinear switched stochastic systems (SSSs) with time-varying delays, where the switching time instants are deterministic rather than stochastic. Herein, the boundedness of the global solution is first proven for highly nonlinear SSSs via the average dwell time (ADT) method and multiple Lyapunov function (MLF) approach. Then, the stability criteria for qth moment exponential stability and almost surely exponential stability are presented. The main difficulty lies in the presence of switching and time-varying delay terms, which prevents the validation of existing methods. New inequality techniques have been developed to counteract the effects of switching signals and time-varying delays. Finally, an example is provided to verify the effectiveness of the results.

Keywords

Highly nonlinear switched stochastic systems / deterministic switching signal / time-varying delays / average dwell time / multiple Lyapunov function