Moment stability in mean square of stochastic delay differential equation

In this paper, we derive a moment stability region in terms of coefficient parameters for a stochastic delay differential equation. Such a stochastic delay equation with both time delay and random effects is an essential model of control systems. As a main result, a fundamental stability problem is solved by delay-dependent stochastic analysis. We adopt the domain-subdivision approach and use Ito's formula in the analysis. For a given time delay, the stability of the stochastic delay differential equation is studied with variable power of noise. It is also shown that an unstable stochastic delay system become stable by an appropriate power of noise. The main results are illustrated by several numerical solutions of the stochastic delay model.