Controllability of linear degenerate difference-differential equations

We consider the initial problem for a control linear time varying system of difference-differential equations with an identically degenerate matrix coefficient of the derivative of the desired vector function in the main part. The sufficient conditions and the necessary and sufficient criterion of full controllability on some segment in the domain of definition are obtained for such a system. The analysis is based on the transformation of the main part to so-called “equivalent form” with separated “differential” and “algebraic” subsystems.