D. Chu; V. Mehrmann : Minimum Norm Regularization of Descriptor Systems by Output Feedback

Author(s) :

D. Chu; V. Mehrmann

Title :

Minimum Norm Regularization of Descriptor Systems by Output Feedback

Electronic source :

[gzipped ps-file] 98 kB
[gzipped dvi-file] 47 kB

Preprint series

Technische Universität Chemnitz-Zwickau, Fakultät für Mathematik (Germany). Preprint 97-6, 1997

Mathematics Subject Classification :

93B05 [ Controllability ]

93B40 [ Computational methods in systems theory ]

93B52 [ Feedback control ]

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

Abstract :

We study the regularization problem for linear, constant coefficient descriptor systems $E x^. = AX + Bu, y_1 = Cx, y_2=\Gamma x^.$ by proportional and derivative mixed output feedback. Necessary and sufficient conditions are given, which guarantee that there exist output feedbacks such that the closed-loop system is regular, has index at most one and $E +BG\Gamma$ has a desired rank, i.e. there is a desired number of differential and algebraic equations. To resolve the freedom in the choice of the feedback matrices we then discuss how to obtain the desired regularizing feedback of minimum norm and show that this approach leads to useful results in the sense of robustness only if the rank of E is decreased. Numerical procedures are derived to construct the desired feedbacks gains. These numerical procedures are based on orthogonal matrix transformations which can be implemented in a numerically stable way.

Keywords :

regularization, mixed outputp, differential and algebraic equations, orthogonal matrix transformation

Language :

english

Publication time :

2/1997