Finite‐time synchronization of network systems with linear and nonlinear couplings via quantized intermittent‐adaptive control

Abstract

This paper investigates the synchronization problem of network systems (NSs) via finite‐time (FIT) control techniques. First, the network systems include two complex networks with linear couplings, nonlinear couplings and different rates of evolution. In order to realize the goal of synchronization, intermittent‐adaptive control schemes with quantizer are designed. Then, several FIT synchronization criteria are established by using the designed controllers whose parameters could be adjusted automatically according to the adaptive laws. At the rest of this article, the numerical simulations are provided to illustrate our results.

Finite‐time bipartite synchronization of T–S fuzzy coupled neural networks via quantized adaptive control

“…Remark In the proof of Theorem 1, inequalities ()–() and () are derived which are different from the corresponding results in earlier studies [8, 11, 21]. Theorem 1 is established via the framework of bipartite synchronization, while some references do not consider bipartite synchronization, for example, previous research [8–11]. …”

“…To derive the main results of the paper, some definitions, lemmas, and assumptions are presented below. Firstly, we give Assumptions 1 and 2 which are usually used in the investigation of bipartite synchronization and state-dependent connection parameters, such as the references [10,11,20,21] and so on. Assumption 1.…”

“…Note that norm is important for studying the dynamical behavior of networks. The FET synchronization results based on the classical FET stability lemma and its variations are always established via 2-norm, while the 1-norm analytical techniques are developed to deal with the FET synchronization of systems with time delays in recent years; one can refer the papers [8,11,14,16,17,21] and other references. In Chen [27], based on the definition of norm, the authors proposed a new norm called generalized norm.…”

“…That is, those parameters are related to the states of systems. For example, coupling strength is assumed as a function of the states in earlier studies [8,9]; state-dependent connection weights are considered in pre-vious research [10,11]. Generally, a lot of practical systems have to face some variable state parameters which can be described by T-S fuzzy CNNs with state-dependent connection weights.…”