This paper is concerned with robust instability analysis for guaranteed persistence of oscillating phenomena in dynamical systems. We first formalize the robust instability analysis problem for single-input-single-output linear time invariant systems by introducing a notion of the robust instability radius (RIR). We provide a method of finding the exact RIR 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 take account of the change of the equilibrium point.
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.
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for guaranteed persistence of oscillating phenomena in
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
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robust instability analysis problem for single-input-single-output linear time invariant
problem for SISO LTI
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of finding the exact RIR
for calculating the RIR exactly
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second-order
second order
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take account of
care for