Fixed-Time Passivity and Synchronization of Spatiotemporal Networks with Multiple Weights via Boundary Control

This article focuses on fixed-time passivity and synchronization for multi-weighted spatiotemporal networks with mixed boundary condition. Firstly, a kind of boundary control scheme is developed, which is implemented on the right boundary. Subsequently, several fixed-time passivity criteria are established by making use of inequality technique and Lyapunov method. In addition, in the light of obtained fixed-time output-strict passivity result, a fixed-time synchronization criterion for the spatiotemporal networks with multiple weights is naturally gained, and the upper bound of the synchronization time is estimated based on fixed-time stability theory. Finally, a simulation example is proposed to verify the availability of the derived results.