Mean-square stability of stochastic differential time-lag systems

Abstract

Two sets of sufficient conditions for the mean-square asymptotic stability of the equilibrium state of linear differential time-lag systems with non-stationary random coefficients are derived. Each of the sets of sufficient conditions is then shown to be equivalent to a corresponding unconstrained optimization problem. Hence, it can readily be solved by standard efficient optimization techniques. The usual trial-and-error method of finding the required parameters to satisfy the stability conditions can now be avoided.