Instability margin analysis for parametrized LTI systems with application to repressilator

Shinji Hara, Tetsuya Iwasaki, Yutaka Hori

Research output: Contribution to journalArticlepeer-review


This paper is concerned with a robust instability analysis for the single-input-single-output unstable linear time-invariant (LTI) system under dynamic perturbations. The nominal system itself is possibly perturbed by the static gain of the uncertainty, which would be the case when a nonlinear uncertain system is linearized around an equilibrium point. We define the robust instability radius as the smallest H norm of the stable linear perturbation that stabilizes the nominal system. There are two main theoretical results: one is on a partial characterization of unperturbed nominal systems for which the robust instability radius can be calculated exactly, and the other is a numerically tractable procedure for calculating the exact robust instability radius for nominal systems parametrized by a perturbation parameter. 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 of our linear robust instability analysis is confirmed by numerical simulations.

Original languageEnglish
Article number110047
Publication statusPublished - 2022 Feb


  • Analysis of systems with uncertainties
  • Instability margin
  • Periodic oscillation
  • Repressilator
  • Robust instability

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering


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