Riccati equations in the stability of retarded stochastic linear systems

Many processes in automatic control, physics, mechanics, biology, economics , etc. can be modeled by stochastic hereditary differential equations. Seve ral results of the theory of stability of these systems and its application s are derived through the Lyapunov functionals. Conditions for the mean-squ are asymptotic stability of stochastic linear differential equations with d iscrete and distributed delay are derived by the special procedure of const ructing Lyapunov functionals developed for studying the stability of functi onal differential and difference stochastic systems. These conditions are f ormulated in terms of the existence of positive-definite solutions of Ricca ti matrix equations.