Exponential Stability Analysis for Stochastic Delayed Differential Systems with Impulsive Effects: Average Impulsive Interval Approach

Abstract

This paper is concerned with the exponential stability analysis of stochastic delayed systems with impulsive effects. By using the average impulsive interval approach, and together with comparison lemma and Razumikhin techniques, sufficient conditions ensuring the moment exponential stability of the systems under consideration are established. A stability criterion for non‐delayed stochastic systems with impulses is also derived as a corollary. Compared with the existing stability results in the literature, which are usually based on the supremum or infimum of impulsive intervals, the results reported in this paper are less conservative. Two illustrative examples are provided to validate the effectiveness and advantages of our theoretical results.

Exponential Lag Synchronization of Memristive Neural Networks with Reaction Diffusion Terms via Neural Activation Function Control and Fuzzy Model

“…In this paper, the problem of exponential lag synchronization of memristive neural networks with reaction diffusion terms via neural activation function control has been firstly investigated. Compared with the results in [17][18][19][20], the results obtained in this paper are more general and more practicable.…”

“…In practical applications, reaction diffusion effect cannot be avoided in the neural network models when electrons are moved by voltage in asymmetric electromagnetic fields, the activation functions and the states of system not only depend on time, but also intensively depend on space in many circumstances. In [17][18][19][20], the stability and synchronization of neural networks with reaction diffusion terms have been considered, it is very important to consider the state of memristive neural network systems varying in space as well as in time. is the state of the ith subsystem, f i and g i is the amplifier, R i is the connection resistors between the amplifier f i ∕g i and state y i (.…”

Exponential Stability and Delayed Impulsive Stabilization of Hybrid Impulsive Stochastic Functional Differential Systems

“…sive stabilization of impulsive stochastic functional differential systems, including impulsive stochastic delay systems, have received a large number of research interests and many results have been reported (see, e.g. [19][20][21][22][23][24]). Specifically, by using Lyapunov functions, some Razumikhin-type theorem on the exponential stability of impulsive stochastic functional differential systems were established in Refs.…”

Exponential stability of hybrid stochastic functional differential systems with delayed impulsive effects: average impulsive interval approach

“…On the other hand, impulsive effects may exist widely in many evolutionary processes in which they experienced changes of state abruptly at certain moments in the fields such as economics, medicine, and biology (see, e.g., [11][12][13][14][15][16][17][18]). More recently, some results on impulsive stochastic functional equations with Markovian switching have been reported in [19][20][21][22][23][24][25] .…”