Finite-time Partial State Components Synchronization Control for Complex Dynamical Networks with Nonidentical Nodes

For a class of complex dynamic networks composed of nonidentical nodes, a decentralized control strategy is proposed to achieve the finite-time partial state components synchronization. The finite-time partial state components synchronization means that only some, not all, state components of each node in the network can achieve synchronization in finite time. Firstly, for the convenience of the theoretical analyses and derivation, a special diagonal matrix is introduced, which can formulate the desired state components of each node. Secondly, based on this special diagonal matrix, the finite-time partial state components synchronization is defined . Compared to the finite-time synchronization, the finite-time partial state components synchronization is more popular. Thirdly, according to both the control theory and the finite-time stability theorem, a decentralized control strategy is proposed, so that our networks can achieve the finite-time partial state components synchronization. Finally, a simulation example is shown to verify the effectiveness and correctness of the proposed control strategy in this paper.