A unified criterion for global exponential stability of quaternion‐valued neural networks with hybrid impulses

Abstract

In this article, the stability of quaternion-valued neural networks (QVNNs) with hybrid impulses is investigated, which contain stabilizing impulses and destabilizing impulses simultaneously. Through constructing the relationship between impulses and quaternions, this article has obtained a unified criterion for the global exponential stability of the system. First, a new form of impulsive representation is constructed, and the established systems can be decomposed into four different real parts. According to the characteristics of the impulses, the system divides the average interval of impulses (AII) into two cases, that is, T < ∞ and T = ∞, which can process hybrid impulses simultaneously. Second, for QVNNs, by using the method of matrix p-norm and the inequality technology, the criterion of each interval is derived. Considering the impulsive effects on the overall stability of QVNNs, the uniform criterion for the global exponential stability can be obtained. In addition, the convergence rate of QVNNs with hybrid impulses is also discussed. Finally, in order to verify the theoretical conclusions, some numerical simulations are given.

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Exponential stability for delayed complex-valued neural networks with reaction-diffusion terms

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Bipartite Synchronization of Heterogeneous Signed Networks with Distributed Impulsive Control

“…ere are some cooperative behaviors of interconnected dynamic systems, such as image processing [1], pattern recognition [2], and secure communication [3], which have been eliciting increasing attention recently. In particular, synchronization, as a typical collective behavior, has been widely studied by many researchers through different control methods, for example, feedback control [4,5], adaptive control [6][7][8], event-triggered control [9][10][11], and impulsive control [12][13][14][15][16][17][18]. Among these methods, impulsive control, as a form of discontinuous control [19], has advantages of low cost and high efficiency and so has been widely used in many fields, such as the population growth model [19] and neural networks [20].…”