Pole Assignment for First Order Linear Systems by Constant Output Feedback

G.I. Kalogeropoulos (Greece), O. Kossak (Ukraine), D.P. Papachristopoulos, and P. Pantazopoulos (Greece)


Output Feedback, Pole Assignment, Matrix Pencils, Canonical Forms, Quadratic Pl¬ucker Relations


In this paper we propose necessary and sufficient condi tions for the solution of the pole assignment problem by constant output feedback, which is associated with the Þrst order linear differential system. The above problem is al ways solvable if the open-loop system is completely con trollable and observable, and is proved to be equivalent to two subproblems, one linear and the other multilinear. So lutions 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 Pl¬ucker relations with only three terms each, which describe com pletely the speciÞc Grassmann variety. Using these re lations one can solve the multilinear problem and conse quently calculate the feedback matrices which give a so lution to the pole assignment problem by constant output feedback. Finally, an illustrative example of the proposed method is given.

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