Abstract
A pinning stabilization problem of complex networks with time-delay coupling is studied under stochastic noisy circumstances in this paper. Only one controller is used to stabilize the network to the equilibrium point when the network is connected and the minimal number of controllers is used when the network is unconnected, where the structure of complex network is fully used. Some criteria are achieved to control the complex network under stochastic noise in the form of linear matrix inequalities. Several examples are given to show the validity of the proposed control criteria.
Highlights
Complex networks have been a major research topic and attracted increasing attention from various fields including physics, biology, sociology, and engineering
We study the stabilization problem of complex networks which can be extended to the synchronization problem
Motivated by the above discussion, we study the pinning stabilization problem on complex networks coupled with time delaying and disturbed by the stochastic noise from three kinds of topology matrices: symmetrical and irreducible, asymmetrical and irreducible, and mreducible
Summary
Complex networks have been a major research topic and attracted increasing attention from various fields including physics, biology, sociology, and engineering. Zhou et al proposed a scheme of determining the number of pinning controlled nodes for general complex networks with positive definite inner coupling [15]. For the coupling matrix being irreducible, the pinning stabilization criteria were proposed in the form of liner matrix inequality for a complex network coupling time delaying [10, 11]. How to select the controlled node for a complex network coupled with time delaying?. Motivated by the above discussion, we study the pinning stabilization problem on complex networks coupled with time delaying and disturbed by the stochastic noise from three kinds of topology matrices: symmetrical and irreducible, asymmetrical and irreducible, and mreducible.
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