Title: Synchronisation scheme for cluster-based interconnected network of nonlinear systems

Authors: Akshay Kumar Jaiswal; Bharat Bhushan Sharma

Addresses: Department of Electrical Engineering, National Institute of Technology, Hamirpur, Himachal Pradesh, India ' Department of Electrical Engineering, National Institute of Technology, Hamirpur, Himachal Pradesh, India

Abstract: The work presented here addresses cluster synchronisation for a class of nonlinear systems using Lyapunov stability theory with nonlinearities satisfying Lipschitz condition. Generally, Lyapunov stability-based adaptive nonlinear control techniques are used to design the controller for nonlinear systems. These techniques are also utilised to address synchronisation in complex interconnected systems. The cluster synchronisation in a complex network of different nonlinear systems is achieved when each state of system of one cluster is synchronised to every corresponding state system of other cluster. Here, using Lyapunov stability theory, a general criterion for cluster synchronisation is obtained. For meeting the goal of synchronisation, bidirectional connections within a cluster and across the clusters are considered. To achieve the results, nonlinearities are assumed to satisfy Lipschitz conditions. The appropriate design of gains for within cluster and across the cluster coupling using Lyapunove stability theory, along with application of Barbalat's lemma, ensure synchronisation of an overall network consisting clusters of dissimilar nonlinear systems. Numerical simulation are presented further for example systems belonging to the considered class of nonlinear systems to verify the efficacy of the proposed approach. For this purpose, cluster of chaotic Lorenz and Lu systems are considered as part of complex network.

Keywords: cluster synchronisation; complex dynamic network; Lyapunov stability; Lipschitz condition.

DOI: 10.1504/IJSCC.2024.135176

International Journal of Systems, Control and Communications, 2024 Vol.15 No.1, pp.1 - 16

Received: 23 Dec 2022
Accepted: 31 May 2023

Published online: 01 Dec 2023 *

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