Computation of supremal (A,B)-invariant and controllability subspaces

Author

Moore, Bruce C. ; Laub, Alan J.

Author_Institution

University of Toronto, Toronto, Canada

Volume

Issue

fYear

1978

fDate

10/1/1978 12:00:00 AM

Firstpage

783

Lastpage

792

Abstract

Two fundamental concepts of geometric control theory, $(A,B)$ -invariant and controllability subspaces, are discussed in terms of spaces spanned by closed-loop eigenvectors. Included is a characterization of $V^{\\ast },R\\Re ^{\\ast }$ , the supremal $(A,B)$ -invariant and controllability subspaces contained in the kernel of some map. Applying ideas found in numerical analysis literature, it is shown that, for design purposes, knowledge of $V^{\\ast },R\\Re ^{\\ast }$ is not sufficient: certain subspaces of $V^{\\ast },R\\Re ^{\\ast }$ may be useless with respect to true design applications. Possible consequences of design based on these unreliable parts of $V^{\\ast },R\\Re ^{\\ast }$ are discussed. Finally, prototype algorithms for computing basis vectors for $V^{\\ast },R\\Re ^{\\ast }$ are given. Their strength is in the additional information which makes it possible to identify the reliable components of $V^{\\ast },R\\Re ^{\\ast }$ Numerical stability and efficiency are "built in" to the algorithms through the use of routines which have been implemented, tested thoroughly, and recommended by recognized experts in numerical analysis.

Keywords

Controllability; Linear systems, time-invariant continuous-time; Control system synthesis; Control theory; Controllability; Hip; Kernel; Laboratories; Numerical analysis; Numerical stability; Prototypes; Testing;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.1978.1101882

Filename

1101882

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=827753