This note 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. Also, the lower bounds of interexecution 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 have been no published papers on the event-triggered control for continuous-time stochastic delay systems. This note is a first try to fill the gap on the topic.

Stabilization of Stochastic Nonlinear Delay Systems With Exogenous Disturbances and the Event-Triggered Feedback Control

Reliable asynchronous sampled-data filtering of T–S fuzzy uncertain delayed neural networks with stochastic switched topologies

In this paper, a novel kind of stochastic delayed complex networks with multi-weights (SDCNMW) is considered. We first split SDCNMW into multiple stochastic complex networks with single weight. This paper is mainly concerned with the issues of exponential stability for SDCNMW. A global Lyapunov functional is constructed by a graph-theoretical approach based on Kirchhoff’s matrix tree theorem. Razumikhin-type theorem is presented by stochastic stability theory and Razumikhin technique. An easy-verified coefficients-type theorem is also given. Finally, theoretical results are illustrated by stochastic oscillators network successfully.

Stability analysis of stochastic delayed complex networks with multi-weights based on Razumikhin technique and graph theory

This paper deals with a state-feedback control scheme for nonlinear stochastic systems with Markovian switching. First, we present the results on the practically $ {p}$ -moment exponential stability with respect to an additional disturbance and the practically $ {p}$ -moment asymptotic stability relying on a specific event. However, elements in this event are hard to be observed directly. The main aim of this paper is to develop a self-triggered sampling rule to overcome this difficulty. By applying the improved monotone growth condition, Ito’s formula, Fubini’s theorem, Gronwall inequality, and comparison lemma, we establish a novel lemma to estimate the lower bound and upper bound of second-moment for state and error, respectively. Moreover, we also establish the practically asymptotic stability in mean square with the help of Jensen’s inequality technique, properties of $ {\mathcal {K}}$ -function and result on $ {p}$ -moment input-to-state stability. Furthermore, from Lipschitz continuity and monotonicity of functions, we obtain the value of the maximum triggering interval based on lasted-observed state. Finally, we give some remarks and discussions to show the significance of our results by comparing with those in the previous literature.

Self-Triggered State-Feedback Control for Stochastic Nonlinear Systems With Markovian Switching

In this short note, we consider time-varying stochastic functional differential systems with distributed-delay dependent impulsive effects Such systems arise from a large number of applications, such as financial markets and population dynamics By developing some inequality techniques and then combining stochastic analysis theory, Lyapunov approach, some stability criteria for such systems are established The feature of the criteria shows that derivatives of the Razumikhin functions are allowed to be indefinite, and the restrictions with respect to the system parameters is very loose Finally, we carry out two numerical experiments to show the usefulness and significance of the criteria

Stability Criteria for Impulsive Stochastic Functional Differential Systems With Distributed-Delay Dependent Impulsive Effects

The authors are concerned with the stability of hybrid stochastic differential equations by feedback controls based on discrete-time state observations. Under some reasonable conditions, they establish an upper bound on the duration τ between two consecutive state observations. Moreover, we can design the discrete-time state feedback control to stabilise the given hybrid stochastic differential equations in the sense of p
th moment exponential stability by developing a new theory. In comparison to the results given in the previous literature, this study has two new characteristics: (i) the stability criterion concerns p
th moment exponential stability, which is different from the existing works; (ii) discrete-time state observations depend on time delays.

https://ietresearch.onlinelibrary.wiley.com/doi/epdf/10.1049/iet-cta.2017.0181

p th moment exponential stabilisation of hybrid stochastic differential equations by feedback controls based on discrete-time state observations with a time delay

Quanxin Zhu

Papers

p th moment exponential stabilisation of hybrid stochastic differential equations by feedback controls based on discrete-time state observations with a time delay