Abstract
In this paper, we study the synchronization problem of continuous-time linear systems under time-varying matrix-weighted coupling. With the help of the notion of persistent excitation and an adapted stability result in adaptive control, we establish two sufficient exponential synchronization conditions using the connectivity of the persistent graph and the joint connectivity of the instantaneous time-varying graphs. The conditions recover those for the single-integrator consensus model with scalar-valued coupling. The results are further applied to solve the synchronization problem of continuous-time linear systems with time-varying and nonidentical coupling matrices, extending the existing conclusions in the literature. Finally, numerical examples are given to verify the derived results.
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