Global Polynomial Stabilization of Impulsive Neural Networks With Bidirectional Proportional Delays

Abstract

The stabilization of a class of impulsive neural networks (INNs) with bidirectional proportional delays (BPDs) is considered. Here, both the INNs and the impulsive conditions are constrained by BPDs. First, the vector form of the INNs with BPDs is presented based on vector properties. A proportional delay-dependent feedback controller is designed, and a novel delay differential inequality (DDI) in vector form is constructed by utilizing the properties of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$M$</tex-math></inline-formula> -matrix and the reduction to absurdity. Under the proposed controller, by using newly established DDI, the properties of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$M$</tex-math></inline-formula> -cone and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$M$</tex-math></inline-formula> -matrix, and matrix spectral radius theory, and it is proved that the equilibrium of studied INNs exists and is unique. And the global exponential stabilization criterion of the equivalent system of studied INNs and its own global polynomial stabilization criterion are obtained. Ultimately, a numerical example involving two cases is listed to test the accuracy for the acquired criteria.