On the complete controllability of hybrid differential-difference systems

Abstract

For time-independent hybrid differential-difference linear systems, we study the complete controllability problem, that is, the problem of complete quieting of such systems. We derive necessary and sufficient parametric conditions for strict complete controllability in various classes of admissible controls. In the case of simplest basic classes, we prove necessary and sufficient parametric conditions for the weak complete controllability and suggest a method for constructing the desired controls quieting the system by using methods of the theory of entire functions of finite degree. We discuss problems of estimating the duration of the transient process. As an example, we consider the strict complete controllability problem in various classes of functions for the case of a system of scalar differential-difference equations.