Pole assignment for first order linear systems by constant output feedback

In this paper we propose necessary and sufficient conditions for the solution of the pole assignment problem by constant output feedback, which is associated with the first order linear differential system. The above problem is always solvable if the open-loop system is completely controllable and observable, and is proved to be equivalent to two subproblems, one linear and the other multilinear. Solutions of the linear problem must be decomposable, that is they lie in an appropriate Grassmann variety. Already known methods compute a reduced set of quadratic Plucker relations with only three terms each, which describe completely the specific Grassmann variety. Using these relations one can solve the multilinear problem and consequently calculate the feedback matrices which give a solution to the pole assignment problem by constant output feedback. Finally, an illustrative example of the proposed method is given.