Book ChapterDOI
The distance between a system and the set of uncontrollable systems
F Rikus Eising
- pp 303-314
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TLDR
A controllability measure in terms of the distance between a system and the set of uncontrollable systems is developed and some properties of a minimal disturbance, rendering a system noncontrollable, are given.Abstract:
A controllability measure in terms of the distance between a system and the set of uncontrollable systems is developed. Some properties of a minimal disturbance, rendering a system noncontrollable, are given.read more
Citations
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Journal ArticleDOI
Stability radii of linear systems
TL;DR: In this paper, the concepts of real and complex stability radii are introduced and some properties of their properties discussed, including their properties in terms of stability and their properties of stability.
Journal ArticleDOI
Between controllable and uncontrollable
TL;DR: The distance between a system (A, B ) and the set of uncontrollable systems is the minimum of the smallest singular value of [λ I − A, B ] with respect to λ.
Journal ArticleDOI
The Multishift QR Algorithm. Part II: Aggressive Early Deflation
TL;DR: A new deflation strategy that takes advantage of matrix perturbations outside of the subdiagonal entries of the Hessenberg QR iterate and identifies and deflates converged eigenvalues long before the classic small-subdiagonal strategy would.
Journal ArticleDOI
Measuring how far a controllable system is from an uncontrollable one
Daniel Boley,Wu-Sheng Lu +1 more
TL;DR: In this article, the authors explore some properties of a controllable system which is near an uncontrollable pair and show to what extent this distance corresponds to certain properties of the uncontrollability matrix and the reachability Grammian.
Journal ArticleDOI
Fast Methods for Estimating the Distance to Uncontrollability
TL;DR: An algorithm based on methods of Gu and Burke-Lewis-Overton that estimates the distance to uncontrollability to any prescribed accuracy is presented, which is an improvement over previous methods which have complexity O(n6), where n is the order of the system.
References
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Journal ArticleDOI
Generalized Inverse of Matrices and Its Applications
TL;DR: In this article, the generalized inverse of matrices and its applications are discussed and discussed in terms of generalized inverse of matrix and its application in the context of generalization of matrix matrices.
Journal ArticleDOI
Properties of numerical algorithms related to computing controllability
TL;DR: The numerical properties of some methods for computing controllability, including the numerical rank of a matrix, the numerical stability of algorithms, the sensitivity of problems, and the scaling of problems are discussed.