Stabilization Of Stochastic Differential Systems Research Articles

Almost sure polynomial stability and stabilization of stochastic differential systems with impulsive effects

In this paper, we first consider the almost surely and pth moment polynomial stability of stochastic differential equations with impulsive effects. Sufficient conditions are given to obtain the polynomial stability. Then the stabilization of stochastic differential systems is studied, which shows that impulse can make stochastic differential equations stable.

Almost sure exponential stability and stochastic stabilization of stochastic differential systems with impulsive effects

This paper focuses on the problem of almost sure exponential stability and stochastic stabilization of nonlinear stochastic differential systems with impulsive effects. The moment stability analysis of impulsive stochastic differential systems has received considerable attention. But relatively little is known about the almost sure exponential stability and noise stabilization. In this paper, by using Lyapunov function, we shall not only establish the general criteria on almost sure exponential stability for general nonlinear impulsive stochastic differential systems but also discuss exact method to design a stochastic perturbation to stabilize a given unstable impulsive differential systems. The efficiency of the proposed results is illustrated by a numerical example.

Dynamic robust stabilization of stochastic differential control systems

The stabilization of stochastic differential control systems by means of dynamic feedback laws is provided. We extend the well-known Artstein–Sontag theorem to derive the necessary and sufficient conditions for the dynamic robust stabilization of stochastic differential systems. An explicit formula for feedback law exhibiting dynamic robust stability in probability is established, and a numerical example is also given to illustrate our results.

A STOCHASTIC JURDJEVIC-QUINN THEOREM FOR THE STABILIZATION OF NONLINEAR STOCHASTIC DIFFERENTIAL SYSTEMS

The purpose of this paper is to state sufficient conditions for the existence of stabilizing state feedback laws for nonlinear stochastic differential systems. This result extends to the stochastic context the well-known theorem of Jurdjevic-Quinn [5] and generalizes previous results on the stabilization of stochastic differential systems.

New results on universal formulas for the stabilization of stochastic differential systems

The aim of this paper is to compute explict formulas for stabilizing feedback laws for nonlinear stochastic differential system for which a control Lapuov function is know The stochastic artstein theorem established previously is extended to deal with control value sets with special forms.