Stabilization of Stochastic Coupled Systems With Time Delay Via Feedback Control Based on Discrete‐Time State Observations

In this paper, we investigate the exponential stability for a class of impulse stochastic differential equations. Different from the previous literature, the impulsive times considered in this paper are random times. By applying stochastic processes theory, stochastic analysis theory and Lyaponov method, we establish several novel exponential stability criteria of the suggested system. Finally, several simple examples are provided to show the validity and significance of the results.

“…[3,12] studied the asymptotic stability for a class of highly nonlinear (neutral) hybrid stochastic systems. More results can be found in [7,9,10,16] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Exponential Stability of Stochastic Differential Equations with Impulse Effects at Random Times

Zhu

2018

“…In the forthcoming paper, we will borrow the idea in the paper to establish a vector form Halanay inequality. Stochastic differential equations arise naturally in a wide variety of applications where uncertainties or random influences, called noises, are taken into account, see for instance, [21][22][23][24][25][26]. We will use the Halanay inequality to study the dynamical behavior of stochastic differential equations in the further.…”

Section: Resultsmentioning

confidence: 99%

The existence and exponential stability of periodic solution for impulsive delay differential equations

Lin

2019

In this work, we first establish a new generalized Halanay inequality with impulses, which have two advantages: one is that impulses can be applied to stabilize the unstable continuous system, the other is that the requirements on the coefficients of inequality are more relaxed than those in previous works. Then, by using the inequality and Banach fixed point theorem, we will obtain some sufficient conditions ensuring the existence and exponential stability of periodic solution for impulsive delay differential equations. The sufficient conditions are easily checked in practice and have a wider adaptive range. Some examples are given to illustrate our results.

“…Up to now, dynamical behaviors of coupled oscillators with or without time‐varying delays have been studied by a considerable number of researchers and some works are reported on their stability and synchronization . To our knowledge, few other authors have studied finite‐time stabilization of coupled oscillators.…”

Section: An Application To Coupled Oscillators With Time‐varying Delamentioning

confidence: 99%

Finite‐Time Stabilization of Coupled Systems on Networks with Time‐Varying Delays via Periodically Intermittent Control

Liu

2018

Self Cite

In this paper, finite-time stabilization of coupled systems on networks with time-varying delays (CSNTDs) via periodically intermittent control is studied. Both delayed subsystems and delayed couplings are considered; the self-delays of different subsystems in delayed couplings are not identical. A periodically intermittent controller is designed to stabilize CSNTDs within finite time, and the stabilization duration is closely related to the topological structures of networks. Furthermore, two sufficient criteria are developed to ensure CSNTDs under periodically intermittent control can be stabilized within finite time by using an approach that combines the Lyapunov method with Kirchhoff's Matrix Tree Theorem. Then finite-time stabilization of coupled oscillators with time-varying delays is given as a practical application and sufficient criteria is obtained. Finally, a numerical simulation is proposed to support our results and show the effectiveness of the controller.