Abstract
Combining impulsive and pinning control, we investigate the synchronization problem of discrete-time network. In the proposed pinning control scheme, the controlled nodes are chosen according to the norm of the synchronization errors at different impulsive instants. Based on the Lyapunov function method and mathematical analysis technique, two synchronization criteria with respect to the impulsive gains and intervals are analytically derived. Both undirected and directed discrete-time networks coupled with Chirikov standard maps are performed in numerical examples to verify the effectiveness of the derived results.
Highlights
1 Introduction Over the past decade, for better modeling and describing the large-scale physical systems consisting of interactive individuals, many kinds of dynamical networks coupled with continuous- or discrete-time dynamical systems have been introduced [ – ]
Since the synchronization errors are time-varying, the pinned nodes become nonidentical at different impulsive instants
We studied the synchronization problem of discrete-time network via impulsive pinning control
Summary
For better modeling and describing the large-scale physical systems consisting of interactive individuals, many kinds of dynamical networks coupled with continuous- or discrete-time dynamical systems have been introduced [ – ]. As an effective control scheme for reducing the number of controlled nodes, has been extensively used to investigate network synchronization, and many valuable results have been obtained [ – ]. Zhang et al [ ] studied pinning control of some typical discrete-time dynamical networks. In [ – ], authors studied synchronization of continuous-time networks through combining impul-
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