Nonfragile Dissipative Synchronization of Reaction-diffusion Complex Dynamical Networks with Coupling Delays

Abstract

This paper focuses on the synchronization of reaction-diffusion complex dynamical networks with coupling delay. In order to reflect the uncertainties of the controller, the nonfragile problem is considered. Furthermore, we also take into account the dissipativity analysis problem, which contains the $$\cal{H}_{\infty}$$ performance and passivity performance in a unified framework. By utilizing the Lyapunov functional method, two sufficient delay-dependent conditions, which ensure the considered system is globally asymptotically synchronized onto the unforced node and strictly dissipative, are established in terms of linear matrix inequality. Finally, three numerical examples are employed to demonstrate the effectiveness of the design methods.