Instability margin analysis for parametrized LTI systems with application to repressilator. (February 2022)

• Record Type: Journal Article
• Authors: Hara, Shinji; Iwasaki, Tetsuya; Hori, Yutaka
• Is Part Of: Automatica. Volume 136(2022)
• Publication Date: 2022-02
• Subjects: Analysis of systems with uncertainties -- Robust instability -- Instability margin -- Periodic oscillation -- Repressilator; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2021.110047
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: 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.