Stability of multi-group coupled systems on networks with multi-diffusion based on the graph-theoretic approach

2016 ◽  
Vol 39 (18) ◽  
pp. 5744-5756 ◽  
Author(s):  
Tianrui Chen ◽  
Jiacheng Xu ◽  
Boying Wu
Keyword(s):  
Coupled Systems ◽  
Theoretic Approach ◽  
Graph Theoretic ◽  
Graph Theoretic Approach

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.

scholarly journals Input-to-state stability of multi-group stochastic coupled systems with time-varying delay

Filomat ◽  
2017 ◽  
Vol 31 (7) ◽  
pp. 2109-2121
Author(s):  
Xiaoling Zou ◽  
Jiacheng Xu
Keyword(s):  
Graph Theory ◽  
Coupled Oscillators ◽  
Coupled Systems ◽  
Theoretic Approach ◽  
Time Varying ◽  
Systematic Method ◽  
Graph Theoretic ◽  
Time Varying Delay ◽  
Graph Theoretic Approach ◽  
Varying Delay

We investigate the issue of p-th moment exponentially input-to-state stability (pMEISS) of multi-group stochastic coupled systems with time-varying delay (MSCSTD) in this paper. By means of results from graph theory, we develop a systematic method that allows one to construct a proper Lyapunov function for MSCSTD. More specifically, two kinds of sufficient criteria, which are called Lyapunov-type and coefficient-type respectively, are derived to ensure pMEISS for MSCSTD by using the graph-theoretic approach. To make results more understandable, we apply them to a typical stochastic coupled oscillators with control inputs.

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