Synchronization of heterogeneous linear networks with distinct inner coupling matrices

• Published in: ISA transactions Vol. 75; pp. 127 - 136
• Main Authors: Liang, Quanyi, Wang, Lei, Hao, Qiqi, She, Zhikun
• Format: Journal Article
• Language: English
• Published: United States Elsevier Ltd 01.04.2018
• Subjects: Distinct inner coupling matrices; Heterogeneous nodes; Invariant set; Synchronization; Distinct inner coupling matrices; Invariant set; Heterogeneous nodes; Synchronization
• ISSN: 0019-0578; 1879-2022
• DOI: 10.1016/j.isatra.2018.01.031

In this paper, we study synchronization of heterogeneous linear networks with distinct inner coupling matrices. Firstly, for synchronous networks, we show that any synchronous trajectory will converge to a corresponding synchronous state. Then, we provide an invariant set, which can be exactly obtained by solving linear equations and then used for characterizing synchronous states. Afterwards, we use inner coupling matrices and node dynamics to successively decompose the original network into a new network, composed of the external part and the internal part. Moreover, this new network can be proved to synchronize to the above invariant set by constructing the corresponding desired Lyapunov-like functions for the internal part and the external part respectively. In particular, this result still holds if the coupling strength is disturbed slightly. Finally, examples with numerical simulations are given to illustrate the validity and applicability of our theoretical results. •For synchronous networks, we show that any synchronous trajectory will converge to a corresponding synchronous state.•By solving linear equations, we obtain a linear invariant subspace to characterize synchronous states.•Based on the above invariant subspace, we decompose the original network into an external part and an internal part and derive a synchronization criterion by constructing corresponding Lyapunov-like functions.