## 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

### Keywords:

controllability measure; uncontrollable systems
Full Text:

### 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., ()
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.