A unified canonical form for controllable and uncontrollable linear dynamical systems†
作者:
C. D. JOHNSON,
期刊:
International Journal of Control
(Taylor Available online 1971)
卷期:
Volume 13,
issue 3
页码: 497-517
ISSN:0020-7179
年代: 1971
DOI:10.1080/00207177108931961
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
A linear transformation is proposed which will transform an arbitrary (constant) linear dynamical systempinto a certain standard (canonical) form. This particular canonical form coincides with the well-known phase-variable canonical form [l]-[5] for the case of completely controllable, scalar input, linear dynamical systems and coincides with a canonical form recently proposed by Luenberger [6] and Wonham [7] in the case of completely controllable, vector input, linear dynamical systems. For linear dynamical systems which are not completely controllable, the canonical form proposed herein displays explicitly: (i) the sub-system ofpwhich is completely controllable and (ii) the sub-system ofpwhich is completely uncontrollable. The explicit identification of these two sub-systems permits us to effectively implement the important fundamental stabilization theorem for constant linear dynamical systems and also a useful theorem on spectrum controllability for linear dynamical systems. An important feature of the present work is the development of an explicit and effective numerical algorithm for computing the required transformation matrix and its inverse
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