This paper is devoted to study the stabilization problem of stochastic nonlinear delay systems with exogenous disturbances and the event-triggered feedback control. By introducing the notation of input-to-state practical stability and an event-triggered strategy, we establish the input-to-state practically exponential mean-square stability of the suggested system. Moreover, we investigate the stabilization result by designing the feedback gain matrix and the event-triggered feedback controller, which is expressed in terms of linear matrix inequalities (LMIs). Also, the lower bounds of inter-execution times by the proposed event-triggered control method are obtained. Finally, an example is given to show the effectiveness of the proposed method. Compared with a large number of results for discrete-time stochastic systems, only a few results have appeared on the event-triggered control for continuous-time stochastic systems. In particular, there has been no published papers on the event-triggered control for continuous-time stochastic delay systems. This work is a first try to fill the gap on the topic.

This paper is concerned with the problem of exponential stability for a class of Markovian jump impulsive stochastic Cohen-Grossberg neural networks with mixed time delays and known or unknown parameters. The jumping parameters are determined by a continuous-time, discrete-state Markov chain, and the mixed time delays under consideration comprise both time-varying delays and continuously distributed delays. To the best of the authors' knowledge, till now, the exponential stability problem for this class of generalized neural networks has not yet been solved since continuously distributed delays are considered in this paper. The main objective of this paper is to fill this gap. By constructing a novel Lyapunov-Krasovskii functional, and using some new approaches and techniques, several novel sufficient conditions are obtained to ensure the exponential stability of the trivial solution in the mean square. The results presented in this paper generalize and improve many known results. Finally, two numerical examples and their simulations are given to show the effectiveness of the theoretical results.

In this paper, the problem of exponential stability is investigated for a class of stochastic neural networks with both Markovian jump parameters and mixed time delays. The jumping parameters are modeled as a continuous-time finite-state Markov chain. Based on a Lyapunov-Krasovskii functional and the stochastic analysis theory, a linear matrix inequality (LMI) approach is developed to derive some novel sufficient conditions, which guarantee the exponential stability of the equilibrium point in the mean square. The proposed LMI-based criteria are quite general since many factors, such as noise perturbations, Markovian jump parameters, and mixed time delays, are considered. In particular, the mixed time delays in this paper synchronously consist of constant, time-varying, and distributed delays, which are more general than those discussed in the previous literature. In the latter, either constant and distributed delays or time-varying and distributed delays are only included. Therefore, the results obtained in this paper generalize and improve those given in the previous literature. Two numerical examples are provided to show the effectiveness of the theoretical results and demonstrate that the stability criteria used in the earlier literature fail.

This paper is devoted to study the Razumikhin stability theorem for a class of impulsive stochastic delay differential systems. By developing a new lemma, stochastic analysis technique and Razumikhin approach, several novel criteria of the $p$th moment exponential stability are derived for the related systems. The key feature of the criteria is that time-derivatives of the Razumikhin functions are allowed to be indefinite, which loosen the constraints of the existing results greatly. Finally, two examples are given to illustrate the usefulness and significance of the theoretical results.