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On the computation of a reduced set of quadratic Plucker relations and their use in the solution of the determinantal assignment problem.

Kalogeropoulos G., Kytagias D.

Systems Science

2000

Vol. 26, nr 2

5-25

An algorithmic method is presented for the computation of a reduced set of quadratic Plucker relations describing completely the Grassmann variety of the corresponding projective space. In particular, it is proven that a set of three terms homogeneous equations can be extracted from the whole set of quadratic Plucker relations. This set contains a specific number of equations, which exactly-constitute a reduced set of quadratic Plucker relations. This is achieved by using a simple criterion based on a correspondence between the coordinates of a decomposable vector and lexicographical orderings. In addition, the algorithm suggested is error-free from numerical computations. The above theory is used for the development of a unifying approach for pole assignment by state and output feedback, for asymptotic observer design and for zero assignment by squaring down for linear time-invariant regular type control systems.