Global Polynomial Synchronization of Proportional Delayed Inertial Neural Networks

Abstract

In this article, the global polynomial synchronization (GPS) using proportional delay inertial neural networks (PDINNs) as a drive-response system is studied. A feedback controller is designed, which is easy to implement in hardware. The order reduction method is used to reduce the error system of the studied systems to the first-order differential equations. The novel proportional delay differential inequalities (DDIs) in norm form are established by applying Lagrange’s mean value theorem, derivative definition, constructing auxiliary function method, and properties of matrix and vector norm. By applying the novel constructed DDIs, two GPS criteria of the studied systems are acquired, which are embodied in the form of matrix norm and are easy to verify. Ultimately, the theoretical results are supported by numerical examples.