Representation of solutions of control hybrid differential-difference impulse systems

We consider linear nonstationary hybrid differential-difference controlled dynamical systems under the action of impulses. For such systems, we derive integral representations of solutions on the basis of the solution of dual (adjoint) systems. This is, in a sense, a generalization to these systems of the Cauchy formula for ordinary systems. This formula is refined in the stationary case. The results are illustrated by an example