Criteria of the mean-square asymptotic stability of solutions of systems of linear stochastic difference equations with continuous time and delay - Korenevsky, D. G. (Ukrains’kyi Matematychnyi Zhurnal, 1998)
We obtain spectral and algebraic coefficient criteria and sufficient conditions for the mean-square asymptotic stability of solutions of systems of linear stochastic difference equations with continuous time and delay. We consider the case of a rational correlation between delays and a “white-noise”-type stochastic perturbation of coefficients. We use the method of Lyapunov functions. Most results are presented in terms of the Sylvester and Lyapunov matrix algebraic equations.