Function projective synchronization in complex dynamical networks with time delay via hybrid feedback control

Adaptive synchronization of the complex dynamical network with non-derivative and derivative coupling

Although function projective synchronization in complex dynamical networks has been extensively studied in the literature, few papers deal with the problem between two different complex networks with correlated random disturbances. In this paper, we present some novel techniques to analyze the problem of synchronization. A probability approach is introduced to obtain an almost sure synchronization criterion. We also present some efficient approaches to analyze the problem of exponential synchronization. For the problem of synchronization in some complex networks, our approaches not only can replace the LaSalle-type theorem but also allow improvements of existing results in the literature. Finally, some numerical examples are provided to demonstrate the effectiveness of the proposed approaches.

This paper focuses on the problem of exponential synchronization of complex dynamical networks (CDNs) with time-varying coupling delay and sampled-data. An improved synchronization criterion is derived for the considered CDNs in terms of the free-weighting matrix method and input delay approach. The design method of the desired sampled-data controller is proposed. The derived result is numerically shown to be less conservative than existing one.

Finite-time synchronization of complex dynamical networks under delayed impulsive effects

This paper investigates the synchronisation of nonlinear coupled complex dynamical networks with different nonlinear nodes and different orders by using decentralised dynamical compensation controllers. We propose a dynamical network mathematical model with similar nonlinear nodes, whose dimensions are different. For this kind of network model, the decentralised dynamical compensation controllers are designed for the state synchronisation of the coupled nodes. In addition, the synchronisation manifold is defined as an invariant manifold, which is regarded as the generalised case of dynamical networks with the same nodes’ dynamics. Furthermore, some stability criteria for the synchronisation are derived by means of rigorous theoretical analysis. Finally, numerical examples are presented to verify the effectiveness of the obtained theoretical results.

Finite-time synchronization of complex dynamic networks with impulsive control and actuator saturation: An LMI approach

This paper addresses the problem of adaptive pinning synchronization of complex dynamical networks with nonlinear delayed intrinsic dynamics and time-varying delays. By introducing decentralized adaptive strategies to both the coupling strengths and the feedback gains, it is proved that the complex dynamical network can synchronize with the desired state for the bounded time-varying delays even when only one node is informed, without any global information of the underlying network. Finally, some numerical simulations are given to verify the main results and show the superiority of these self-designed adaptive strategies.

This paper studies the problem of sampled-data exponential synchronization of complex dynamical networks (CDNs) with time-varying coupling delay and uncertain sampling. By combining the time-dependent Lyapunov functional approach and convex combination technique, a criterion is derived to ensure the exponential stability of the error dynamics, which fully utilizes the available information about the actual sampling pattern. Based on the derived condition, the design method of the desired sampled-data controllers is proposed to make the CDNs exponentially synchronized and obtain a lower-bound estimation of the largest sampling interval. Simulation examples demonstrate that the presented method can significantly reduce the conservatism of the existing results, and lead to wider applications.

Function projective synchronization in complex dynamical networks with or without external disturbances via error feedback control

This paper deals with the synchronization problem of complex dynamical networks with interval time-varying coupling delays. A simple local linear feedback controller is introduced to guarantee the synchronizability of the networks. Some delay-dependent synchronization conditions for the controlled complex dynamical networks are presented by using the Lyapunov–Krasovskii functional method and the reciprocally convex combination approach. Theoretical analysis and numerical examples show that the obtained conditions have less computational complexity and less conservatism than some recently reported ones.

Network topology and node dynamics play a key role in forming synchronization of complex networks. Unfortunately there is no effective synchronization criterion for pinning synchronization of complex dynamical networks with switching topology. In this paper, pinning synchronization of complex dynamical networks with switching topology is studied. Two basic problems are considered: one is pinning synchronization of switched complex networks under arbitrary switching; the other is pinning synchronization of switched complex networks by design of switching when synchronization cannot achieved by using any individual connection topology alone. For the two problems, common Lyapunov function method and single Lyapunov function method are used respectively, some global synchronization criteria are proposed and the designed switching law is given. Finally, simulation results verify the validity of the results.

On designing decentralized impulsive controllers for synchronization of complex dynamical networks with nonidentical nodes and coupling delays

A novel criterion for cluster synchronization of complex dynamical networks with coupling time-varying delays

The improved synchronization of complex dynamical networks under passivity performance is the main topic of this paper. To distinguish between simple and complex dynamics in real-world scenarios, the effect of randomly occurring time-varying delays is specifically considered. The study is based on the development of a feedback controller and a Lyapunov-Krasovskii functional (LKF) with novel integral terms. Finally, a useful example is provided to illustrate the effectiveness of the proposed approach.

Exponential estimates and sufficient conditions for the exponential synchronization of complex dynamical networks with bounded time-varying delays are given in terms of linear matrix inequalities (LMIs). A generalized complex networks model involving both neutral delays and retarded ones is presented. The exponential synchronization problem of the complex networks is converted equivalently into the exponential stability problem of a group of uncorrelated delay functional differential equations with mixed time-varying delays. By utilizing the free weighting matrix technique, a less conservative delay-dependent synchronization criterion is derived. An illustrative example is provided to demonstrate the effectiveness of the proposed method.