Exponential Stability of Stochastic Highly Nonlinear Delayed Systems With Regime-Switching Diffusion Under Asynchronous Intermittent Control

This article explores the application of asynchronous intermittent control (AIC) in stochastic highly nonlinear delayed systems (SHNDSs) with regime-switching diffusion, and studies the pth moment exponential stability of the controlled systems. For SHNDSs that no longer satisfy linear growth conditions but rather polynomial growth conditions, a new Lyapunov functional is constructed, which includes both pth power and qth power terms (q>p≥ 2). In addition, this article introduces AIC into SHNDSs due to the independent response of each node, which leads to traditional Halanay inequalities no longer being applicable. To address this, we introduce an auxiliary timer to the new constructed Lyapunov functional. By taking the Dupire’s functional derivatives, combined with the Dupire’s functional Itô formula for regime-switching and graph theory methods, the negative-definiteness of LV is successfully ensured in both the working interval and the resting interval of the control cycle, effectively guaranteeing the stability of the systems. As a result, some criteria for the pth moment exponential stability of SHNDSs under AIC are provided. Finally, the theoretical results are utilized in the analysis of the stochastic delayed van der Pol-Duffing oscillators with regime switching, while the simulation results confirm the efficacy of these findings.