A graph-theoretic method to stabilize the delayed coupled systems on networks based on periodically intermittent control

2017 ◽  
Vol 40 (18) ◽  
pp. 6760-6775 ◽  
Author(s):  
Beibei Guo ◽  
Yu Xiao ◽  
Chiping Zhang
Keyword(s):  
Coupled Systems ◽  
Intermittent Control ◽  
Theoretic Method ◽  
Periodically Intermittent Control ◽  
Graph Theoretic

scholarly journals Graph-Theoretic Approach to Exponential Stability of Delayed Coupled Systems on Networks under Periodically Intermittent Control

2018 ◽  
Vol 23 (1) ◽  
pp. 44-63
Author(s):  
Beibei Guo ◽  
Yu Xiao ◽  
Chiping Zhang
Keyword(s):  
Exponential Stability ◽  
Type Theorem ◽  
Sufficient Conditions ◽  
Coupled Systems ◽  
Intermittent Control ◽  
Theoretic Approach ◽  
Periodically Intermittent Control ◽  
Graph Theoretic ◽  
Graph Theoretic Approach ◽  
Close Relationship

In this paper, the exponential stability of delayed coupled systems on networks (DCSNs) is investigated via periodically intermittent control. By utilizing graph-theoretic approach and Lyapunov function method, a novel method for stability analysis of DCSNs is developed. Moreover, some useful and easily verifiable sufficient conditions are presented in the form of Lyapunov-type theorem and coefficients-type criterion. These laws reveal that the stability has a close relationship with the topol- ogy structure of the networks. In addition, as a subsequent result, the obtained theory is successfully applied to study the exponential stability of delayed coupled oscillators on networks under periodically intermittent control. Finally, a numerical example is given to validate the effectiveness of theoretical results.

Periodically intermittent control for synchronized stationary distribution and synchronization of memristor-based stochastic coupled systems

2019 ◽  
Vol 41 (14) ◽  
pp. 4142-4156
Author(s):  
Yan Liu ◽  
Wenxue Li ◽  
Kaiwen Feng ◽  
Huihui Song
Keyword(s):  
Stationary Distribution ◽  
Control Strategy ◽  
Coupled Oscillators ◽  
Lyapunov Method ◽  
Coupled Systems ◽  
Intermittent Control ◽  
Periodically Intermittent Control ◽  
A New Technique ◽  
First Time ◽  
Theoretical Results

This article is concerned with inner synchronized stationary distribution for memristor-based stochastic coupled systems for the first time. It is worth mentioning that periodically intermittent control that serves as a new technique is introduced into the investigation of synchronized stationary distribution. Based on the graph theory, the Lyapunov method and periodically intermittent control strategy, two main theorems that guarantee the existence of a synchronized stationary distribution are obtained, whose results illustrate that the existing region of synchronized stationary distribution depends on the control rate, coupled strength and so on. On the other hand, exponential synchronization is also taken into consideration and a theorem is presented. In addition, as applications, memristor-based stochastic coupled oscillators and stochastic coupled Chua’s circuits are presented to verify the practicability of theoretical results. Finally, two simulation examples are given to demonstrate the effectiveness and feasibility of theoretical results.

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