Passivity for undirected and directed fractional-order complex networks with adaptive output coupling

In this paper, the passivity for adaptive output coupled fractional-order complex networks (CNs) under undirected and directed topologies is studied by selecting appropriate coupling weight adjustment strategies, based on which the output synchronization for the presented networks is discussed by leveraging the properties of Mittag-Leffler functions and the Laplace transform technique. Utilizing the developed distributed adaptive schemes, several passivity criteria for the fractional-order CNs with output coupling are derived. Moreover, several output synchronization conditions for the output coupled fractional-order CNs are given by employing the acquired passivity results. Ultimately, simulations from numerical examples are utilized to judge the effectiveness for the adaptive laws and the presented criteria.