Distance Problems for Linear Dynamical Systems

Daniel Kressner () and Matthias Voigt ()
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Daniel Kressner: ANCHP, EPF Lausanne
Matthias Voigt: Technische Universität Berlin, Institut für Mathematik

Chapter Chapter 20 in Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory, 2015, pp 559-583 from Springer

Abstract: Abstract This chapter is concerned with distance problems for linear time-invariant differential and differential-algebraic equations. Such problems can be formulated as distance problems for matrices and pencils. In the first part, we discuss characterizations of the distance of a regular matrix pencil to the set of singular matrix pencils. The second part focuses on the distance of a stable matrix or pencil to the set of unstable matrices or pencils. We present a survey of numerical procedures to compute or estimate these distances by taking into account some of the historical developments as well as the state of the art.

Keywords: Singular Vector; Hamiltonian Matrix; Left Eigenvector; Imaginary Eigenvalue; Matrix Pencil (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-15260-8_20

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DOI: 10.1007/978-3-319-15260-8_20

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