Sampled-data exponential synchronization of complex dynamical networks with time-varying coupling delay.

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

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.

In this paper, in the case of quantized communication and coupling delays, a novel quantized pinning control (QPC) law is designed to deal with the synchronization problem of complex dynamic networks (CDN). Utilizing the Lyapunov method, non-smooth analysis tools and convex combination techniques, some sufficient criteria for achieving synchronization of CDNs with coupling delays are given. Finally, the effectiveness of the main results is demonstrated by presenting a simulation example.

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

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.

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.

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 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.

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

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

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.

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

Exponential synchronization for coupled complex networks with time-varying delays and stochastic perturbations via impulsive control

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

In this paper, the problem of combination projection synchronization of fractional-order complex dynamic networks with time-varying delay couplings and external interferences is studied. Firstly, the definition of combination projection synchronization of fractional-order complex dynamic networks is given, and the synchronization problem of the drive-response systems is transformed into the stability problem of the error system. In addition, time-varying delays and disturbances are taken into consideration to make the network synchronization more practical and universal. Then, based on Lyapunov stability theory and fractional inequality theory, the adaptive controller is formulated to make the drive and response systems synchronization by the scaling factors. The controller is easier to realize because there is no time-delay term in the controller. At last, the corresponding simulation examples demonstrate the effectiveness of the proposed scheme.