Stability analysis for a class of complex dynamical networks with 2-D dynamics

Abstract

In this paper, the problems of stability and decentralized control are studied for a class of linear coupled dynamical networks with Fornasini---Marchesini second local state-space dynamics. Necessary and sufficient stability conditions are obtained for a class of linear network composed by $$N$$ identical nodes. Effects of the interconnection on stability of network are presented by eigenvalues of the topological matrix, and the effectiveness of interconnection on network stability is pointed out. Moreover, the decentralized control laws are presented for two types of linear regular networks: star-shaped coupled networks and globally coupled networks in detail. The relationships between the stability of a network and the stability of its corresponding nodes are studied. It is shown that some nodes must be made stable in order to stabilize the whole network in some cases. However, the detailed relationship is needed to be further investigated.