Stability analysis of stochastic highly nonlinear delayed systems with regime-switching,multi-links and distributed delay under intermittent control

Abstract

In this paper, we aim to study the mean exponential stability of stochastic highly nonlinear delay system with regime-switching diffusion, multi-links and distributed delay under aperiodic intermittent control. To address the stability challenges posed by high nonlinearity, multiple time delays, stochastic disturbances, complex network topology, and abrupt mode switching, we propose an effective solution as follows: Novel Lyapunov functionals containing both quadratic term and q-power term ( $q\ge 2$ ) of state variables are constructed, and the auxiliary timers are designed to avoid the discontinuity of control. By combining graph theory, Dupire’s functional derivatives and Dupire’s functional Itô formula, we successfully prove that the infinitesimal generator $\mathbb{L}\mathcal{V}$ is strictly negative defined on the working period and resting period of control, respectively, and then derive the sufficient conditions ensuring mean exponential stability. The key constraints include strongly connected graph structure, strict inequalities of Lyapunov function coefficients, strict inequalities of growth restrictions on coupling functions and distributed delay, and average working time ratio, respectively. The stochastic delayed FitzHugh–Nagumo system with state-switching is applied, and the aperiodic intermittent control is designed, where the numerical simulation results indicate the effectiveness of our results.