Abstract
In this paper, the stability and stabilization issues for a class of delayed neural networks with time-varying hybrid impulses are investigated. The hybrid effect of two types of impulses including both stabilizing and destabilizing impulses is considered simultaneously in the analysis of systems. To characterize the occurrence features of impulses, the concepts of average impulse interval and average impulse strength are employed. Based on the analysis of stability, a pinning impulsive controller which can ensure the global exponential stability of the studied neural networks is designed by pinning a small fraction of neurons. Finally, two numerical examples are given to illustrate the effectiveness of the proposed control schemes for delayed neural networks with hybrid impulses.
Highlights
During the past few decades, dynamic networks have been systematically studied due to their broad application background in different areas [1,2,3,4,5,6,7,8,9]
Time delays frequently appear in various dynamical systems [20, 21]. e existence of time delays in neural networks may induce more complex dynamical behaviors such as instability, oscillations, and chaos [22,23,24,25,26,27]. erefore, it is necessary to investigate effects of time delays and impulses on the stability of neural networks
Stabilizing impulses can be considered as impulsive controllers, which can enhance the stabilization of dynamical systems
Summary
During the past few decades, dynamic networks have been systematically studied due to their broad application background in different areas [1,2,3,4,5,6,7,8,9]. In [43], some adequate conditions that can ensure the exponential synchronization of inertial memristor-based neural networks with time delay were given by utilizing the average impulsive interval approach. En, based on the Lyapunov method combined with the utilization of proper mathematical analysis techniques, the stability analysis for neural networks with time-varying delays and hybrid impulses is carried out. Under this circumstance, the classification of stabilizing and destabilizing impulses is not taken into account; just the overall effect of the impulses is taken into consideration. A pinning impulsive controller design procedure for the stabilization of the investigated neural networks is proposed based on the above analysis. Given τ > 0, C([− τ, 0], Rn) denotes the family of continuous functions from [− τ, 0] to Rn
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