Abstract
In this paper, we consider an evolution linear control system. First, by using Weiss–Staffans perturbation results we prove that, under suitable conditions, our evolution system is well posed. Next, we give a characterisation of observability of the evolution system via some spectral condition. We also provide sufficient condition to ensure the stability of the system in the periodic case. As applications, we consider concrete problems including wave equation in one dimension.
Disclosure statement
No potential conflict of interest was reported by the author(s).