MATRIX RICCATI EQUATIONS AND STABILITY OF STOCHASTIC LINEAR SYSTEMS WITH NONINCREASING DELAYS
Vladimir B. Kolmanovskii, Leonid E. Shaikhet · Functional Differential Equations · 2004
Many real processes can be modeled by stochastic differential equations with aftereffect [1]-[3]. Stability conditions for such systems can be obtained by construction of appropriate Lyapunov functionals using special procedure of Lyapunov functionals construction [4]-[14]. In this paper asymptotic mean square stability of stochastic linear differential equations with discrete and distributed delays is considered. Stability conditions are formulated in terms of existence of positive definite solutions of matrix Riccati equations. The method of different Riccati equations construction is proposed.