Volker Mehrmann; Hongguo Xu : An Analysis of the Pole Placement Problem II. The Multi-Input Case

Author(s) :

Volker Mehrmann; Hongguo Xu

Title :

An Analysis of the Pole Placement Problem II. The Multi-Input Case

Electronic source:

application/pdf

Preprint series

Technische Universität Chemnitz-Zwickau, Fakultät für Mathematik (Germany). Preprint 97-14, 1997

Mathematics Subject Classification :

65F15 [ Eigenvalues (numerical linear algebra) ]

65F35 [ Matrix norms, etc. (numerical linear algebra) ]

65G05 [ Roundoff error ]

93B05 [ Controllability ]

93B55 [ Pole and zero placement problems ]

Abstract :

For the solution of the mulit-input pole placement problem we derive explicit formulas for the subspace from which the feedback gain matrix can be chosen and for the feedback gain as well as the eigenvector matrix od the closed-loop system. We discuss which Jordan structures can be assigned and also when diagonalizability can be achived. Based on these formulas we study the conditioning of the pole-placement problem in terms of perturbations in the data and show how the conditioning depends on the condition number of the closed loop eigenvector matrix, the norm of the feedback matrix and the distance to uncontrollability.

Keywords :

pole placement, contition number, perturbation theory, Jordan form, explicit formulas, Cauchymatrix, Vandermonde matrix, stabilization, feedback gain, distance to uncontrollability

Language :

english

Publication time :

5/1997

Notes :

Research Grant Me 790/7-2