2020/08/25 by Shinji Hara, Tetsuya Iwasaki, Hara, Shinji +3
Biochemistry, Genetics and Molecular Biology · Engineering · #Control and Stability of Dynamical Systems #FOS: Biological sciences #FOS: Electrical engineering #Gene Regulatory Network Analysis #Microbial Metabolic Engineering and Bioproduction #Quantitative Methods (q-bio.QM) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2008.10983
openalex publication_date 2020/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.