Instability margin analysis for parametrized LTI systems with application to repressilator

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 itself possibly perturbed by static gain of uncertainty, which would be case when nonlinear uncertain linearized around an equilibrium point. We define radius as smallest H ∞ norm stable perturbation that stabilizes system. There are two main theoretical results: one on partial characterization unperturbed systems can calculated exactly, and other numerically tractable procedure calculating exact parametrized parameter. results applied to repressilator in synthetic biology , where hyperbolic unique guarantees persistence oscillation phenomena global sense, effectiveness our confirmed numerical simulations.