Dwell time for local stability of switched affine systems with application to non-spiking neuron models
Dwell time for local stability of switched affine systems with application to non-spiking neuron models
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DOI：
10.1016/j.aml.2018.06.026
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发表时间：
2018-12-01
影响因子：
3.7
通讯作者：
Phung，Anthony
中科院分区：
文献类型：
--
作者：
Makarenkov，Oleg;Phung，Anthony
对于在不同的全局稳定平衡点之间切换的切换系统，我们提供了将振荡锁定在平衡点所需邻域的封闭形式公式。在非尖峰神经元模型的激励下，本文主要关注平面切换仿射系统的情况，其中我们使用了来自二次李雅普诺夫函数的嵌套柱体的性质。特别地，我们第一次使用驻留时间的概念来给出具有周期性开关电流的线性神经元模型的无尖峰的明确条件。
For switched systems that switch between distinct globally stable equilibria, we offer closed-form formulas that lock oscillations in the required neighborhood of the equilibria. Motivated by non-spiking neuron models, the main focus of the paper is on the case of planar switched affine systems, where we use properties of nested cylinders coming from quadratic Lyapunov functions. In particular, for the first time ever, we use the dwell-time concept in order to give an explicit condition for non-spiking of linear neuron models with periodically switching current.