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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.

The pole-assignment problem for positive linear discrete-time systems with scalar controls

James D.J., Rumchev V.G.

Systems Science

2002

Vol. 28, nr 2

15-27

The paper considers the pole-assignment problem on the basis of the single-input positive linear discrete-time systems, compares it with the unrestricted case and develops procedures for finding a linear state-feedback controller that assigns the spectrum of the closed-loop to the desired spectrum

Some remarks on pole assignability of distributed parameter systems

Kobayashi T.

Archives of Control Sciences

1998

Vol. 7, no. 1/2

33-41

The pole assignment problem of distributed parameter systems with unbounded feedback is discussed. The problem can be solved under a weaker restriction between the open-loop poles { lambda /sub n/} and the closed-loop poles { beta /sub n/}. Two types of the expression of a characteristic equation whose roots are the closed-loop poles are first given. Next a feedback element is given which realizes the desired pole assignment of the closed-loop system. An interesting result is shown that an infinite number of the open-loop poles { lambda /sub n/} can be shifted such that | lambda /sub n/- beta /sub n/|=O(| lambda /sub n/|/sup (1- epsilon /2)/) ( epsilon : sufficiently small positive number) for all n.