Stability of discrete-time stochastic complex networks with impulses under an almost sure framework

As an extension of continuous-time scenarios, this paper focuses on the almost sure stability of discrete-time stochastic complex networks (DSCNs) with impulses. Therein, a complete non-uniformly distributed activation-sleep impulsive strategy (CNAIS) is employed where the impulsive signals are only considered within a nonperiodic working window rather than the entire time. Applying the Lyapunov method, stochastic analysis theory, almost sure stability criteria of DSCNs with CNAIS, corresponding to the mode-independent average impulsive interval and mode-dependent one respectively, are established directly by exploiting the advantageous consequences of noise, where the traditional assumption of mean square stability is removed Notably, for non-impulsive moments, the existing results necessitate the convergence of the Lyapunov function in the moment sense under impulsive interferences. This type of Lyapunov function may be difficult to guarantee for certain systems whose diffusion term serves as a control input It is notable to underscore that the stability criteria developed overcome the above limitation. Then it enables the applications in assessing the stability of the systems that cannot conform to the Lyapunov functions with moment sense convergence at non-impulsive moments, even if impulses are jamming signals. Finally, the feasibility is illustrated by simulation examples.