Exponential synchronization of switched complex dynamical networks with simultaneously triangularizable coupling matrices

Abstract

Exponential synchronization of directed complex dynamical networks with switching topology and switching inner coupling matrices are studied via the switched system stability theory. Firstly, under the assumption that all subnetworks are synchronizable, we propose sufficient conditions to maintain local synchronization under the average dwell time scheme. Secondly, when not all subnetworks are synchronizable, it is shown that in addition to average dwell time, if the ratio of the total activation time of synchronizable and non-synchronizable subnetworks satisfies an extra condition, the local synchronization of the switched network is also guaranteed. Then, we extend the local results to the global case where the network's isolated dynamics satisfies specific conditions. Our results could explain the sustainability of synchronization of complex dynamical networks against "successful" but recoverable attacks. The assumption of simultaneous diagonalizability of the coupling matrices is no longer needed. Instead, the coupling matrices need only to be simultaneously similarly triangularizable. Numerical examples are given to demonstrate the effectiveness of the proposed results.