Quasi sure exponential stabilisation of impulsive stochastic complex networks under a sublinear expectation framework

Abstract

In this paper, we explore quasi sure exponential stabilisation of impulsive stochastic complex networks under a sublinear expectation framework – impulsive stochastic complex networks driven by G-Brownian motion (G-ISCNs). In contrast with the existing literature, by combining graph theory, Lyapunov method and average impulsive interval method, some sufficient conditions for quasi sure exponential stabilisation of G-ISCNs are obtained, which removes the commonly premised assumption that the system is moment stable. Moreover, in virtue of the method based on supremum and infimum of impulsive interval, quasi sure exponential stabilisation criterion of G-ISCNs is established under discussing the following three cases, respectively: (1) the continuous dynamics is stable; (2) the impulsive dynamics is stable; (3) the impulse is inactive. Then the theoretical results are applied to impulsive coupled oscillators systems driven by G-Brownian motion, and the corresponding criterion is gained, which is substantiated with a numerical example finally.