Finite-Time Passivity and Synchronization of Complex Dynamical Networks With State and Derivative Coupling

Quasi-synchronization for variable-order fractional complex dynamical networks with hybrid delay-dependent impulses

This paper focuses on addressing the problem of quasi-synchronization in heterogeneous variable-order fractional complex dynamical networks (VFCDNs) with hybrid delay-dependent impulses. Firstly, a mathematics model of VFCDNs with short memory is established under multi-weighted networks and mismatched parameters, which is more diverse and practical. Secondly, under the framework of variable-order fractional derivative, a novel fractional differential inequality has been proposed to handle the issue of quasi-synchronization with hybrid delay-dependent impulses. Additionally, the quasi-synchronization criterion for VFCDNs is developed using differential inclusion theory and Lyapunov method. Finally, the practicality and feasibility of this theoretical analysis are demonstrated through numerical examples.

Robust Passivity and Control for Directed and Multiweighted Coupled Dynamical Networks

In this article, the passivity and control issues for directed uncertain coupled dynamical networks are solved. The presented model is directly coupled with multiple coupling matrices and parametric uncertainty, while previous literatures of multiweighted networks usually suppose that outer coupling matrices (OMs) are connected, undirected, and certain. The viewpoint of inner coupling matrices (IMs) in this article is added and OMs can be directed and not connected, which is a great improvement on the existing results. First, for all diagonal IMs, considering each dimension separately, we can derive if the weighted combination of multiple OMs for each dimension is strongly connected, then passivity and pinning control rules can be established. In addition, we also discuss the situation that IMs are positive definite but not diagonal. By means of the weighted combination of normalized left eigenvectors (NLEVec) corresponding to zero eigenvalue for multiple coupling matrices, we prove if the Chebyshev distance (Cheb-Dist) among these NLEVec is less than a tolerant deviation interval, then passivity, synchronization, and pinning control criteria are acquired. Moreover, a matter of adaptive coupling strengths is also settled. Examples are provided to verify the validity of established results.

Finite-Time Passivity and Synchronization of Multi-Weighted Complex Dynamical Networks Under PD Control

This article focuses on finite-time passivity (FTP) and finite-time synchronization (FTS) for complex dynamical networks with multiple state/derivative couplings based on the proportional-derivative (PD) control method. Several criteria of FTP for complex dynamical networks with multiple state couplings (CDNMSCs) are formulated by utilizing the PD controller and constructing an appropriate Lyapunov function. Furthermore, FTP is further used to investigate the FTS in CDNMSCs under the PD controller. In addition, the FTP and FTS for complex dynamical networks with multiple derivative couplings (CDNMDCs) are also studied by exploiting the PD control method and some inequality techniques. Finally, two numerical examples are worked out to demonstrate the validity of the presented PD controllers.

Finite-Time Output Synchronization of Undirected and Directed Coupled Neural Networks With Output Coupling

This article focuses on the finite-time output synchronization problem for undirected and directed coupled neural networks with output coupling (CNNOC). Based on the designed state feedback controllers and some inequality techniques, we present several finite-time output synchronization criteria for these network models. In addition, two kinds of coupling-weight adjustment strategies are also developed to guarantee the finite-time output synchronization of undirected and directed CNNOC. Finally, two numerical examples are also provided to demonstrate the effectiveness of the theoretical results.

Stability of delayed inertial neural networks on time scales: A unified matrix-measure approach

This note introduces a unified matrix-measure concept to study the stability of a class of inertial neural networks with bounded time delays on time scales. The novel matrix-measure concept unifies the classic matrix-measure and the generalized matrix-measure concept. One sufficient global exponential stability criterion is obtained based on this key matrix-measure and no Lyapunov function is required. To make the stability performance better, another stability criterion in which more detailed information is involved has been acquired. The theoretical results in this note contain and extend some existing continuous-time and discrete-time works. A numerical example is given to show the validity of the results.

Finite-time and fixed-time anti-synchronization of Markovian neural networks with stochastic disturbances via switching control

This paper proposes a unified theoretical framework to study the problem of finite/fixed-time drive-response anti-synchronization for a class of Markovian stochastic neural networks. State feedback switching controllers without the sign function are designed to achieve the finite/fixed-time anti-synchronization of the addressed systems. Compared with the existing synchronization criteria, our results indicate that the controllers via the switching control without the sign function are given with less conservativeness, and the controllers without any sign function can deal with the chattering problem. By employing Lyapunov functional method and properties of the Weiner process, several finite/fixed-time synchronization criteria are presented and the corresponding settling times are calculated as well. Finally, three numerical examples are provided to illustrate the effectiveness of the theoretical results.