Before revision:  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 .
After revision:  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 .