Boundary Control-Based Finite-Time Passivity for Fractional Spatiotemporal Directed Networks with Multiple Weights

This article mainly delves into finite-time passivity and finite-time synchronization of fractional-order spatiotemporal directed networks with multiple weights via boundary control schemes. Firstly, several concepts of finite-time passivity for fractional spatiotemporal models are proposed by virtue of a fractional-order differential inequality. Next, a boundary controller is presented to realize the passivity, which only relies on the information of the state at the spatial boundary. Subsequently, by constructing the Lyapunov function and leveraging some inequality techniques, some sufficient conditions in the form of linear matrix inequalities are established to ensure the finite-time strict passivity, finite-time input strict passivity, and finite-time output strict passivity. As a consequence of the derived result of finite-time output strict passivity, several criteria are obtained for realizing finite-time synchronization of the addressed fractional spatiotemporal networks. A numerical example is eventually presented to verify the developed control protocol and the theoretical criteria.