Improved almost sure stability criteria of stochastic complex-valued dynamical networks with hybrid impulses

Abstract

In this paper, exponential stability of stochastic complex-valued dynamical networks with hybrid impulses is considered. Therein, different from the existing works on the moment stability of stochastic complex-valued systems, almost sure exponential stability is studied, in which noise contributes to the stability of the system. Hybrid impulses, which allows that a kind of impulsive sequence includes stabilizing and destabilizing impulses simultaneously, are first exerted on stochastic complex-valued networks. In light of Lyapunov method, stochastic analysis theory, average impulsive interval and average impulsive gain, we establish improved almost sure exponential stability criteria under the two situations that average impulsive interval Ta satisfies Ta<+∞ and Ta=+∞ separately. The stability criteria we addressed possess two characteristics as follows. Firstly, time-derivatives of the Lyapunov functions are permitted to be indefinite, even unbounded, based on indefinite Lyapunov functions, which results in lower conservative consequence. Secondly, it is worth noting that the mutual restrains among average impulsive gain, average impulsive interval and the noise intensity are represented in the improved criteria. Besides, the theoretical results are directly applied to study the stability of stochastic systems with aperiodically intermittent noise. Finally, an application to inertial complex-valued neural networks and several numerical examples are provided to show the feasibility and advantages of the theoretical results.