This brief investigates globally exponential synchronization for linearly coupled neural networks (NNs) with time-varying delay and impulsive disturbances. Since the impulsive effects discussed in this brief are regarded as disturbances, the impulses should not happen too frequently. The concept of average impulsive interval is used to formalize this phenomenon. By referring to an impulsive delay differential inequality, we investigate the globally exponential synchronization of linearly coupled NNs with impulsive disturbances. The derived sufficient condition is closely related with the time delay, impulse strengths, average impulsive interval, and coupling structure of the systems. The obtained criterion is given in terms of an algebraic inequality which is easy to be verified, and hence our result is valid for large-scale systems. The results extend and improve upon earlier work. As a numerical example, a small-world network composing of impulsive coupled chaotic delayed NN nodes is given to illustrate our theoretical result.

The asymptotic synchronization of coupled reaction-diffusion neural networks with proportional delay and Markovian switching topologies is considered in this brief where the diffusion space does not need to contain the origin. The main objectives of this brief are to save communication resources and to reduce the conservativeness of the obtained synchronization criteria, which are carried out from the following two aspects: 1) mode-dependent quantized control technique is designed to reduce control cost and save communication channels and 2) Wirtinger inequality is utilized to deal with the reaction-diffusion terms in a matrix form and reciprocally convex technique combined with new Lyapunov-Krasovskii functional is used to derive delay-dependent synchronization criteria. The obtained results are general and formulated by linear matrix inequalities. Moreover, combined with an optimal algorithm, control gains with the least magnitude are designed.

This study presents a detailed survey on recent development of logical networks and its applications, including the background of logical networks, the theory of a new matrix product called semi‐tensor product (STP) of matrices, some fundamental works on logical networks, and some current research works. Particularly, some fundamental works on logical networks are presented for the past years, including controllability, stability and stabilisation, synchronisation, disturbance decoupling and so on. Due to the great potential of STP in dealing with logical networks, a surge of attraction from overseas is paid on the study of STP and its applications. Currently, some new research areas are widely studied including pinning control, function perturbations, system decomposition, trajectory control, output tracking issues, symbolic dynamics and so on. The main concern of this study is to present a comprehensive introduction to logical networks and some other applications under the framework of STP of matrices.

This article investigates global exponential synchronization almost surely (GES a.s.) of complex networks (CNs) with node delay and switching topology. By introducing transition probability (TP) and mode-dependent average dwell time (MDADT) to the switching signal, the considered model is more practical than the systems with average dwell-time (ADT) switching. Controllers with both impulsive effects and actuator fault feedback are considered. New analytical techniques are developed to obtain sufficient conditions to guarantee the GES a.s. Different from the existing results on the synchronization of switched systems, our results show that the GES a.s. can still be achieved even in the case that the upper bound of the dwell time (DT) of uncontrolled nodes is very large and the lower bound of the DT of controlled nodes is very small. Numerical examples demonstrate the effectiveness and the merits of the theoretical analysis.

The globally exponential synchronization problem for general dynamical networks is considered in this paper. One quantity will be distilled from the coupling matrix to characterize the synchronizability of the corresponding dynamical networks. The calculation of such a quantity is very convenient even for large-scale networks. The network topology is assumed to be directed and weakly connected, which implies that the coupling configuration matrix can be asymmetric, weighted, or reducible. This assumption is more consistent with the realistic network in practice than the constraint of symmetry and irreducibility. By using the Lyapunov functional method and the Kronecker product techniques, some criteria are obtained to guarantee the globally exponential synchronization of general dynamical networks. In addition, numerical examples, including small-world and scale-free networks, are given to demonstrate the theoretical results. It will be shown that our criteria are available for large-scale dynamical networks.

In the paper, we investigate the exponential stability of nonlinear delayed systems with destabilizing and stabilizing delayed impulses, respectively. Specifically, the study can be divided into tw...