On the Almost Sure Stability of Linear Stochastic Systems

Abstract

Sufficient conditions guaranteeing the almost sure asymptotic stability of linear dynamical systems described by stochastic differential equations are obtained via a straightforward but useful generalization of the Caughey–Gray Lyapunov-type technique. The computational framework consists of a parameterization of the Lyapunov-type norm and the application of an optimization scheme. A fourth-order system is employed as an illustration and comparison with deterministic results is furnished.