The Stability and Stabilization of Stochastic Delay-Time Systems

Abstract EN

The aim of this paper is to investigate the stability and the stabilizability of stochastic time-delay deference system.

To do this, we use mainly two methods to give a list of the necessary and sufficient conditions for the stability and stabilizability of the stochastic time-delay deference system.

One way is in term of the operator spectrum and H-representation; the other is by Lyapunov equation approach.

In addition, we introduce the notion of unremovable spectrum of stochastic time-delay deference system, describe the PBH criterion of the unremovable spectrum of time-delay system, and investigate the relation between the unremovable spectrum and the stabilizability of stochastic time-delay deference system.