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Pole assignment for higher order linear systems: an algorithmic method

Kalogeropoulos G. I., Papachristopoulos D. P.

Systems Science

2005

Vol. 31, no 4

5-20

In this paper, we propose an algorithmic method for a solution of the pole assignment problem which is associated with a higher order linear system, in the case it is completely controllable. The above problem is proved to be equivalent to two subproblems, one linear and the other multilinear. Solutions of the linear problem must be decomposable vectors, that is, they lie in an appropriate Grassmann variety. The method proposed computes 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. Finally, an illustrative example of the algorithmic procedure proposed is given.

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.