Stability of Stochastic Delay Differential Systems With Variable Impulses Due to Logic Choice

Abstract

This paper is concerned with stability problems of stochastic delay differential systems with variable impulses due to logic choice. Firstly, a class of variable impulses due to logic choice is introduced in this paper which is more general than the logic impulses established in [20] and [21]. Then, by establishing a connection between the stochastic delay differential system with logic impulses and a corresponding stochastic delay differential system without logic impulses, some sufficient conditions for stability of the systems are obtained. Finally, the application in a class of linear stochastic delay differential systems with logic impulses is discussed, and several stability criteria together with two numerical examples are given.

Stability of Differential Systems with Impulsive Effects

“…This situation changed after the semi-tensor product method was proposed in [100], which can transform logical functions into equivalent algebraic expressions. Against this background, the differential systems with impulses suffered by logic choice have attracted the attention of some researchers in recent years, see [101][102][103][104][105][106][107][108][109].…”

“…Furthermore, refs. [106,107] extended the research work of the impulses suffered by logic choice to stochastic systems, and the sufficient conditions for stability in [107] are relatively easy to verify because they do not contain Lyapunov functions.…”

Uniform Stability of Linear Delay Impulsive Differential Systems With Impulse Time Windows and Logic Choice

“…[25] obtained the stability criteria for linear delay differential systems under logic impulsive control. [26] investigtated stability problems of stochastic delay differential logic impulse systems. But to our best of knowledge, at present, systems with these two properties have not been studied.…”