Graph-theoretic approach to exponential synchronization of coupled systems on networks with mixed time-varying delays

2017 ◽  
Vol 354 (12) ◽  
pp. 5067-5090 ◽  
Author(s):  
Beibei Guo ◽  
Yu Xiao ◽  
Chiping Zhang
Keyword(s):  
Exponential Synchronization ◽  
Coupled Systems ◽  
Theoretic Approach ◽  
Time Varying ◽  
Graph Theoretic ◽  
Graph Theoretic Approach

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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