Passivity analysis and pinning control of multi-weighted complex dynamical networks

A multi-weighted network model with different dimensions of output and input vectors is studied in this paper. First, we analyze the passivity of the proposed network model by employing some inequality techniques and Lyapunov functional method, and give a synchronization condition for output-strictly passive complex dynamical network with multi-weights (CDNMWs). Furthermore, by using pinning adaptive strategies to control a small portion of nodes or edges, some sufficient conditions for ensuring passivity of CD-NMWs are presented. In addition, when CDNMWs under the designed pinning adaptive control strategies are output-strictly passive, two synchronization criteria are also established. Finally, two examples are given to show the validity of the obtained results.