On the perturbation of the observability equation in linear control systems

The aim of this paper is to investigate stability and sensitivity of the observability variable in linear control systems, (LCS) for short. We first present two results of Hölder continuity in the abstract framework of the ordinary differential equation initial-value problem x′(t) = f(t,x(t)),x(t ₀) = x ₀. Afterwards, we apply our results to automatic systems, providing henceforth the sharpest bounds for the parametric input-output relation in LCS.