Finite-time projective synchronization between two different complex networks

In this paper, the finite-time stochastic outer synchronization between two different complex dynamical networks with noise perturbation is investigated. By using suitable controllers, sufficient conditions for finite-time stochastic outer synchronization are derived based on the finite-time stability theory of stochastic differential equations. It is noticed that the coupling configuration matrix is not necessary to be symmetric or irreducible, and the inner coupling matrix need not be symmetric. Finally, numerical examples are examined to illustrate the effectiveness of the analytical results. The effect of control parameters on the settling time is also numerically demonstrated.

This paper investigates the problem of finite-time function projective synchronization in complex multi-links networks with time-varying delay. A nonlinear feedback controller is designed to achieve finite-time function projective synchronization. Some novel and useful finite-time function projective synchronization criteria are derived based on finite-time stability theory. And another controller is designed to ensure function projective synchronization of complex multi-links networks with time-varying delay. Finally, illustrative examples are given to show the feasibility of the proposed method.

Synchronization stability in complex interconnected neural networks with nonsymmetric coupling

This paper is concerned with the problem of finite-time synchronization for a class of discrete-time semi-Markovian jumping complex dynamical networks (CDNs) with actuator faults based on reliable control. The main aim of this paper is to design a state feedback controller such that the resulting closed-loop system is finite-time synchronized under a prescribed dissipativity performance level even in the presence of actuator failures. Moreover, a stochastic nature followed by Bernoulli distribution is described in the considered networks due to the occurrence of probabilistic nature in time-varying delays. By composing a suitable Lyapunov–Krasovskii functional containing triple summation terms with the aid of Kronecker product properties, Lyapunov stability theory and free weighting matrix approach, sufficient criteria are established in terms of linear matrix inequalities that assure finite-time synchronization and meet the dissipativity performance to the addressed CDNs. The usefulness of the presented design scheme is finally verified by numerical examples.

Finite-time mixed outer synchronization of complex networks with time-varying delay and unknown parameters

In this paper, finite-time synchronization (FTS) problems in an array of unified chaotic and hyperchaotic systems are mainly studied using some important control methods. First, FTS and finite-time transmission synchronization (FTTS) for N systems are realized in a finite time by designing the effective control schemes, and the stability criteria can be given. The corresponding examples are presented to show the effectiveness and feasibility of the controllers proposed by considering three chaotic and hyperchaotic systems.

Robust synchronization in finite time for fractional-order hybrid coupling discontinuous complex dynamic networks with nonlinear growth

Finite-time and fixed-time bipartite synchronization of complex networks with signed graphs

Many canonical and modern control problems can be recast into the problem of solving a group of matrix inequalities. Some of them are in the form of linear matrix inequalities (LMIs), which can be solved very efficiently by the powerful LMI toolbox in Matlab, but some others are in the form of quasi LMIs (QLMIs). By quasi, we mean that unknown parameters are involved in the matrix inequalities and these inequalities are LMIs only when the unknown parameters are fixed. Thus how to guess the unknown parameters is the key to solve the whole problem. In this paper, we present an optimal estimate for the unknown parameters. We will illustrate our method by completely solving the problems of overshoot bound control and reachable set analysis for uncertain systems. Numerical examples are provided to show the effectiveness of the proposed method.

Exploring synchronizability of complex dynamical networks from edges perspective

Adaptive finite-time projective synchronization of complex networks with nonidentical nodes and quantized time-varying delayed coupling

Synchronization control of switched linearly coupled neural networks with delay

<p>In this article, the finite time anti-synchronization (FTAS) of master-slave 6D Lorenz systems (MS6DLSS) is discussed. Without using previous study methods, by introducing new study methods, namely by adopting the properties of quadratic inequalities of one variable and utilizing the negative definiteness of the quadratic form of the matrix, two criteria on the FTAS are achieved for the discussed MS6DLSS. Up to now, the existing results on FTAS of chaotic systems have been achieved often by adopting the linear matrix inequality (LMI) method and finite time stability theorems (FTST). Adopting the new study methods studies the FTAS of the MS6DLSS, and the novel results on the FTAS are gotten for the MS6DLSS, which is innovative study work.</p>

This paper studies the outer synchronization problem of discrete fractional complex networks (DFCNs) with and without the presence of unknown topology. A discrete complex network with a fractional difference is first established and analyzed. By constructing a suitable Lyapunov function and utilizing properties of the fractional difference, outer synchronization criteria for the DFCNs with and without unknown topology are established based on linear matrix inequalities. Meanwhile, the unknown parameters in the topology structure of the network can be identified by adaptive update laws. In the end, two numerical examples are given to exemplify the validity and applicability of the obtained results.

This paper addresses the problem of stability analysis for a class of uncertain discrete-time stochastic BAM neural networks with time-varying delays and impulses. In this paper, we assume that stochastic disturbances are described by the Brownian motion and jumping parameters are generated from discrete-time discrete-state homogeneous Markov process. By employing the Lyapunov–Krasovskii functional and stochastic analysis theory, a set of novel sufficient conditions are derived to guarantee the robust global exponential stability of the equilibrium point in the mean square. The obtained results are shown to be less conservative than the existing one in the literature. Note that the obtained results are formulated in terms of linear matrix inequality (LMI) that can efficiently solved by the LMI toolbox in Matlab. Numerical examples are given to show that the proposed result significantly improve the allowable upper bounds of delays over some existing results in the literature.