The admissible control problem from the moment problem point of view

The admissible control problem occupies an important place in control theory. This problem involves the study of the set of all   bounded controls which solve a given control problem, including the time optimal control. In this work we show with the help of the Fundamental Matrix Inequality of Potapov that the solution of the admissible control problem for the canonical linear case can be given in terms of the solution of a classical Hausdorff moment problem on a finite interval [0,θ][0,θ].