Aperiodically intermittent stabilization for hybrid stochastic differential equations with pantograph delay

Abstract This paper addresses the problem of using aperiodically intermittent control (AIC) to stabilize hybrid stochastic differential equations with pantograph delay (HSDEwPDs). The AIC, which is based on the average control rate, makes the obtained results less conservative. It is noteworthy that the delay type considered in most existing literature, which focuses on delay systems with AIC, is constant delay or bounded time‐varying delay, which renders the existing methods ineffective in studying HSDEwPDs with AIC. Thus, a novel Halanay‐type inequality lemma is developed to serve HSDEwPDs with AIC. By utilizing the Lyapunov functions and ‐matrix, two sufficient criteria are derived to ensure the exponential stability of HSDEwPDs with AIC. Moreover, the theoretical findings are applied to stochastic pantograph oscillators with Markovian switching. Eventually, a numerical example and associated simulations are offered to check the validity of our theory.