Abstract

This article addresses the problem of synchronization on secure communications in complex dynamical networks (CDNs) with the time-varying coupling delay using delay-dependent feedback control. To enhance the security of communication between the main system and each node of CDNs, the n-shift cipher, a cryptographic technique designed to encrypt plain signals, and a public key are used to encrypt the original information signal transmitted from the main system. After fully accounting for the nonlinear function, a unique Lyapunov-Krasovskii functional (LKF) is developed. Subsequently, new criteria are derived using novel integral inequalities and the reciprocally convex combination method to handle the derivative of the LKF, which is finally formulated in terms of linear matrix inequality (LMI). These criteria recover the original information signal on each CDNs node and ensure stable synchronization, thus facilitating secure communication among all nodes of the main system and CDNs. The efficacy and merits of the synchronization criteria are demonstrated using Chua's circuit in four distinct scenarios.