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

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 Rossler systems to test and validate the obtained theoretical results.(c) 2022 Elsevier Ltd. All rights reserved.

Automated summary

This paper presents a novel controller technique for network synchronization of chaotic systems with time-varying delay. The technique achieves stabilization and synchronization of complex chaotic systems by employing an appropriate Krasovskii-Lyapunov functional and fast switching topology. The controller is designed asynchronously, taking into account the time-varying delays in order to avoid instability and performance degradation of the systems. The study demonstrates that the robust controller considers uncertainties and achieves exact synchronization by switching the action of the controller and the dynamics of the chaotic nodes of the studied systems. Numerical examples on chaotic Rossler systems are provided to validate the theoretical results.