On stabilization of a class of systems with time proportional delay

In this paper, we investigate a possibility of the linear difference-differential system stabilization with time proportional delay by the linear observation. Using the sufficient conditions of asymptotic stability for the linear systems with linearly increasing delay, we obtain some conditions of the asymptotic evaluation system existence for the original system. Then we use the asymptotic evaluation system for the construction of the stabilizing control and derive the sufficient conditions for the existence of such control.