The Graded Hautus Test of Controllability for 2-D Systems

It is well-known that the Hautus test of controllability of 2-D systems results in two distinct cases of controllability, namely, when the cancelation variety is empty and when it is zero-dimensional. While the case of the empty cancelation variety has a distinctive trajectory level interpretation -...

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Bibliographic Details
Published in:IEEE control systems letters 2024, Vol.8, p.490-495
Main Authors: Pal, Debasattam, Zerz, Eva
Format: Article
Language:English
Subjects:
Aerospace electronics
Algebraic/geometric methods
Controllability
distributed parameter systems
Image representation
Kalman filters
Kernel
Linear systems
Trajectory
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Summary:It is well-known that the Hautus test of controllability of 2-D systems results in two distinct cases of controllability, namely, when the cancelation variety is empty and when it is zero-dimensional. While the case of the empty cancelation variety has a distinctive trajectory level interpretation - i.e., existence of an observable image representation - the case of the zero-dimensional cancelation variety lacks such an interpretation. We show in this letter that the idea of factoring the system's equations by a linear principal ideal of equations provides this missing trajectory level interpretation.
ISSN:2475-1456
2475-1456
DOI:10.1109/LCSYS.2024.3397036