A Uniqueness Theorem for Linear Control Systems with Coinciding Reachable Sets

Two multivariable linear control systems are considered with control $u(t)$ satisfying the inequality $\| {u(t)} \|_p \leqq 1$, $1 \leqq p \leqq \infty $, and with coinciding reachable sets. Under certain conditions (of which $p \ne 2$ seems to be the most remarkable), it is shown that the control s...

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Bibliographic Details
Published inSIAM journal on control Vol. 11; no. 3; pp. 412 - 416
Main Authors Hautus, M. L. J., Olsder, G. J.
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.08.1973
Subjects
Coordinate transformations
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Summary:Two multivariable linear control systems are considered with control $u(t)$ satisfying the inequality $\| {u(t)} \|_p \leqq 1$, $1 \leqq p \leqq \infty $, and with coinciding reachable sets. Under certain conditions (of which $p \ne 2$ seems to be the most remarkable), it is shown that the control systems have equal system matrices and equal control matrices up to the signs and the ordering of the columns. The proof depends on a theorem of Banach on rotations.
ISSN:0036-1402
0363-0129
1095-7138
DOI:10.1137/0311033