Robust stabilization and synchronization in a network of chaotic systems with time-varying delays

Abstract

In this paper, a novel controller technique is derived for the network synchronization of chaotic systems with time-varying delay. The stabilization of the complex chaotic systems is achieved by considering an appropriate Krasovskii-Lyapunov functional in order to find the asynchronous robust stabilization law and fast switching topology. In a similar way, the asynchronous technique is based on an appropriate switching topology in order to synchronize the chaotic systems. The time-varying delays occur in different systems which increase the complexity of the synchronization. So for this reason, an asynchronous controller is designed by considering the time-varying delays in order to avoid instability or deteriorate performance of the whole chaotic systems. The remarkable finding of this study is that the robust controller considers the uncertainties on each complex chaotic systems node until an exact synchronization is achieved while switching the action of the controller synchronization and the chaotic node dynamics of the studied complex systems. Finally, numerical examples are considered on chaotic Rössler systems to test and validate the obtained theoretical results.