Dealing with impulsive effects is one of the most challenging problems in the field of fixed-time control. In this paper, we solve this challenging problem by considering fixed-time synchronization of complex networks (CNs) with impulsive effects. By designing a new Lyapunov function and constructing comparison systems, a sufficient condition formulated by matrix inequalities is given to ensure that all the dynamical subsystems in the CNs are synchronized with an isolated system in a settling time, which is independent of the initial values of both the CNs and the isolated system. Then, by partitioning impulse interval and using the convex combination technique, sufficient conditions in terms of linear matrix inequalities are provided. Our synchronization criteria unify synchronizing and desynchronizing impulses. Compared with the existing controllers for fixed-time and finite-time techniques, the designed controller is continuous and does not include any sign function, and hence, the chattering phenomenon in most of the existing results is overcome. An optimal algorithm is proposed for the estimation of the settling time. Numerical examples are given to show the effectiveness of our new results.

This paper considers the global exponential synchronization of drive-response memristive neural networks (MNNs) with heterogeneous time-varying delays. Because the parameters of MNNs are state-dependent, the MNNs may exhibit unexpected parameter mismatch when different initial conditions are chosen. Therefore, traditional robust control scheme cannot guarantee the synchronization of MNNs. Under the framework of Filippov solution, the drive and response MNNs are first transformed into systems with interval parameters. Then suitable controllers are designed to overcome the problem of mismatched parameters and synchronize the coupled MNNs. Based on some novel Lyapunov functionals and interval matrix inequalities, several sufficient conditions are derived to guarantee the exponential synchronization. Moreover, adaptive control is also investigated for the exponential synchronization. Numerical simulations are provided to illustrate the effectiveness of the theoretical analysis.

This technical correspondence considers finite-time synchronization of dynamical networks by designing aperiodically intermittent pinning controllers with logarithmic quantization. The control scheme can greatly reduce control cost and save both communication channels and bandwidth. By using multiple Lyapunov functions and convex combination techniques, sufficient conditions formulated by a set of linear matrix inequalities are derived to guarantee that all the node systems are synchronized with an isolated trajectory in a finite settling time. Compared with existing results, the main characteristics of this paper are twofold: 1) quantized controller is used for finite-time synchronization and 2) the designed multiple Lyapunov functions are strictly decreasing. An optimal algorithm is proposed for the estimation of settling time. Numerical simulations are provided to demonstrate the effectiveness of the theoretical analysis.

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 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.