Moment stability in mean square of stochastic delay differential equation

Abstract

Abstract-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.

Asymptotic Mean Square Stability Analysis for a Stochastic Delay Differential Equation

“…In [7] and [8], the authors also showed that the influence of time delay can be reduced by noise for a scalar stochastic delay system with particular parameters. They used the so-called domain subdivision approach [9] together with the Ito's formula to derive the stability regions in terms of the parameters of a given equation and to deal with the fluctuation noise.…”

Convergence and Confidence Intervals of Sample Paths of a Stochastic Differential Equation

“…For an end-fixed inverted pendulum, it was shown that stability is enhanced by the existence of noise with appropriate power [3]. The authors showed that the influence of time delay can be reduced by noise for a scalar stochastic delay system [4,5].…”