On delay-dependent stability for discrete nonlinear stochastic systems with state delay and Volterra diffusion term

Global asymptotic stability conditions for discrete nonlinear scalar stochastic systems with state delay and Volterra diffusion term are obtained based on the convergence theorem for semiMartingale inequalities, without assuming the Lipschitz conditions for nonlinear drift functions. The derived stability conditions are directly expressed in terms of the system coefficients. A nontrivial example of a nonlinear system satisfying the obtained stability conditions is given. The obtained results are compared to some previously known asymptotic stability conditions for discrete nonlinear stochastic systems