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- W3081443689 abstract "Instability of an equilibrium point often provides a basis for an oscillatory mode of operation in certain nonlinear dynamical systems. This paper is concerned with a fundamental robustness analysis for instability of an equilibrium point in the presence of a dynamic perturbation. Our analysis is based on the linearized system around the equilibrium point, which may move due to the perturbation. We define the instability margin as the infimum of the $H_infty$ norm of the stable linear perturbation that exponentially stabilizes the corresponding equilibrium point. There are two main theoretical results; one is on characterizations of linear systems for which the robust instability radius can be calculated exactly and the other is on the exact instability margin for a class of nonlinear systems by properly taking the change of the equilibrium point into account. The results are applied to the Repressilator in synthetic biology, where hyperbolic instability of a unique equilibrium guarantees the persistence of oscillation phenomena in the global sense, and the effectiveness is confirmed by numerical simulations." @default.
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- W3081443689 date "2020-08-25" @default.
- W3081443689 modified "2023-09-27" @default.
- W3081443689 title "Instability Margin Analysis with Application to Biological Oscillations." @default.
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