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Between controllable and uncontrollable. (English) Zbl 0542.93007
Summary: The distance between a system (A,B) and the set of uncontrollable systems is the minimum of the smallest singular value of [\(\lambda\) I-A,B] with respect to \(\lambda\).

MSC:
93B05 Controllability
15A18 Eigenvalues, singular values, and eigenvectors
15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
93C05 Linear systems in control theory
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References:
[1] Paige, C.C., Properties of numerical algorithms related to computing controllability, IEEE trans. automat. control, 26, 1, (1981) · Zbl 0463.93024
[2] Eising, R.; Eising, R., The distance between a system and the set of uncontrollable systems, (), also in · Zbl 0534.93011
[3] Golub, G.H.; Van Loan, C.F., ()
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