A theorem on the strong asymptotic stability and determination of stabilizing controls

Abstract

In this work we show the role which plays a recent theorem on the strong asymptotic stability [17,14,1] in the analysis of the strong stabilizability problem in Hilbert spaces. We consider a control system with skew-adjoint operator and one-dimensional control. We examine in details the property for a linear feedback control to stabilize such a system. A robustness analysis of stabilizing controls is also given.