Synchronization Criterion and Control Scheme for Lur'e Type Complex Dynamical Networks with Switching Topology and Coupling Time‐Varying Delay

Abstract

In this paper, the synchronization problem is addressed in the context of Lur'e type complex switched network (CSN) with coupling time-varying delay in which every node is a Lur'e system. Based on the Lyapunov-Krasovskii theory and linear matrix inequality (LMI) technique, a delay-dependent synchronization criterion and a decentralized state feedback dynamic controller for synchronization of CSNs have been proposed. By choosing a common Lyapunov-Krasovskii functional and using the combined reciprocal convex technique, some previously ignored terms can be reconsidered and less conservative conditions can be obtained. In addition, by using an eigenvalue-decoupling method and convex optimization theory, highdimension LMIs are decoupled into a set of low-dimension ones and the computation complexity of the criterion can be significantly reduced. The effectiveness and applicability of the suggested control solution is verified and assessed through the analysis for two numerical examples.

Absolute stability of switched Lurie systems via dwell time switching

“…A significant subtype is the one composed by switched Lurie systems, which are depicted by a feedback junction of a switched linear system and a nonlinearity bounded by a sector. Actually, many nonlinear control problems can be converted to switched Lurie systems, such as model predictive control, 9 Hopfield neural networks, 10 variable structure systems, 11 sensor network problems, 12 and so on. [13][14][15] In the study of Lurie systems, the stability plays an important role, and the stability of Lurie systems is often called absolute stability.…”

Synchronization of Complex Dynamical Networks with Dynamical Behavior Links

“…Synchronization has been also developed in man-made systems such as chaos-based secure communication networks, distributed computing systems, and harmonic oscillation generation in human heartbeat regulation [10]. For this purpose, various synchronization problems have been defined including complete synchronization [11,12], lag synchronization [13], local synchronization [14], cluster synchronization [15], and projective synchronization [16]. Manuscript The ability of complex dynamical networks (CDN) to model real-world problems encourages researchers to develop CDNs from two broad perspectives: (i) Dynamic model of the nodes; (ii) How to connect the nodes.…”

“…Synchronization has been also developed in man‐made systems such as chaos‐based secure communication networks, distributed computing systems, and harmonic oscillation generation in human heartbeat regulation . For this purpose, various synchronization problems have been defined including complete synchronization , lag synchronization , local synchronization , cluster synchronization , and projective synchronization .…”

Synchronization Criteria for Complex Dynamical Networks with State and Coupling Time‐Delays

“…Complex dynamical networks with time‐delay in the states of dynamical nodes have been rarely studied. In and , synchronization criterion for Lur'e type complex dynamical networks is considered with time‐delay in the states of the nodes and the coupling delay, respectively. To the best of the author's knowledge, almost all of the published papers have only considered the coupling delay for the network, but the state delay could exist in the nodes of the network.…”