TY - GEN
T1 - Robust Instability Analysis with Application to Neuronal Dynamics
AU - Hara, Shinji
AU - Iwasaki, Tetsuya
AU - Hori, Yutaka
N1 - Funding Information:
This work was supported in part by the Ministry of Education, Culture, Sports, Science and Technology in Japan through Grant-in-Aid for Scientific Research (A) 21246067 and (B) 18H01464. S. Hara is with Tokyo Institute of Technology, Shinji Hara@ipc.i.u-tokyo.ac.jp, T. Iwasaki is with University of California Los Angels, tiwasaki@ucla.edu, Y. Hori is with Keio University, yhori@appi.keio.ac.jp.
Publisher Copyright:
© 2020 IEEE.
PY - 2020/12/14
Y1 - 2020/12/14
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85099875946&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85099875946&partnerID=8YFLogxK
U2 - 10.1109/CDC42340.2020.9304320
DO - 10.1109/CDC42340.2020.9304320
M3 - Conference contribution
AN - SCOPUS:85099875946
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 6156
EP - 6161
BT - 2020 59th IEEE Conference on Decision and Control, CDC 2020
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 59th IEEE Conference on Decision and Control, CDC 2020
Y2 - 14 December 2020 through 18 December 2020
ER -