Robust Instability Analysis with Application to Neuronal Dynamics
Systems and Control
2021-01-28 v3 Systems and Control
Neurons and Cognition
Abstract
This paper is concerned with robust instability analysis of linear feedback systems subject to a dynamic uncertainty. The work is motivated by, and provides a basic foundation for, a more challenging problem of analyzing persistence of oscillations in nonlinear dynamical systems. We first formalize the problem for SISO LTI systems by introducing a notion of the robust instability radius (RIR). We provide a method for calculating the RIR exactly for a certain class of systems and show that it works well for a class of second order systems. This result is applied to the FitzHugh-Nagumo model for neuronal dynamics, and the effectiveness is confirmed by numerical simulations, where we properly care for the change of the equilibrium point.
Keywords
Cite
@article{arxiv.2003.01868,
title = {Robust Instability Analysis with Application to Neuronal Dynamics},
author = {Shinji Hara and Tetsuya Iwasaki and Yutaka Hori},
journal= {arXiv preprint arXiv:2003.01868},
year = {2021}
}