DocumentCode :
827753
Title :
Computation of supremal (A,B)-invariant and controllability subspaces
Author :
Moore, Bruce C. ; Laub, Alan J.
Author_Institution :
University of Toronto, Toronto, Canada
Volume :
23
Issue :
5
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 :
بازگشت