A nine-fold canonical decomposition for linear systems
作者:
H. ALING,
J. M. SCHUMACHER,
期刊:
International Journal of Control
(Taylor Available online 1984)
卷期:
Volume 39,
issue 4
页码: 779-805
ISSN:0020-7179
年代: 1984
DOI:10.1080/00207178408933206
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
The zero structure for non-minimal proper systems in state-space form is investigated. The approach is ‘ geometric ’, and a complete characterization in geometric terms is given of the invariant, decoupling, system and transmission zeros, as defined by Rosenbrock. The first main result is a formula for the transmission zeros. Second, a ‘ canonical ’ lattice diagram is presented of a decomposition of the state space which can be viewed as the ‘ product ’ of the Kalman canonical decomposition and the Morse canonical decomposition. This decomposition gives a straightforward characterization of all zeros just mentioned in terms of spectral properties of subspaces under a certain class of feedback and injection mappings. Via this diagram a number of equivalent formulae for the transmission zeros are derived. The freedom in pole assignment leads to new characterizations for the invariant and system zeros in terms of greatest common divisors of characteristic polynomials. Finally, the relation is demonstrated between certain subspaces and some structural invariants, i.e. the zeros at infinity and the minimal indices of a polynomial basis for the kernel of the transfer function.
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