Noises for Impulsive Differential Systems

Abstract

Stochastic feedback control has aroused folks' notice, but little is known on the roles of stochastic noises for the dynamic behavior of impulsive differential systems. In this paper, we mainly study the problem of stochastic stabilization on explosive solutions of nonlinear impulsive differential systems by noises. Under the one-sided polynomial growth condition, a nonlinear impulsive differential system may explode at a finite time. To suppress the explosive solution, we introduce two independent stochastic noises (polynomial and linear) such that there exists a unique global solution for the corresponding stochastically perturbed impulsive differential system, and the global solution is bounded and almost surely exponentially stable.

Exponential Stability for a Class of Linear Delay Differential Systems Under Logic Impulsive Control

“…On the other hand, due to the importance of theory and application, impulsive system has always been the focus of many researchers (see [8]- [33] and references therein). From the perspective of the research topics on impulsive systems, in addition to periodic solutions [8], oscillation [9], noise [10], etc., various kinds of stability have also been studied extensively. For example, exponential stability [11], practical stability [12], interval stability [13], finitetime stability [14], numerical stability [15] and so on.…”