Pseudospectral components and the distance to uncontrollability

J. V. Burke; A. S. Lewis; M. L. Overton

doi:10.1137/S0895479803433313

Pseudospectral components and the distance to uncontrollability

J. V. Burke, A. S. Lewis, M. L. Overton

Research output: Contribution to journal › Article › peer-review

Abstract

We show that 2-norm pseudospectra of m-by-n matrices have no more than 2m(4m-1) connected components. Such bounds are pertinent for computing the distance to uncontrollability of a control system, since this distance is the minimum value of a function whose level sets are pseudospectra. We also discuss algorithms for computing this distance, including a trisection variant of Gu's recent algorithm, and we show how these may be used to locally maximize the distance to uncontrollability for a parameterized system.

Original language	English (US)
Pages (from-to)	350-361
Number of pages	12
Journal	SIAM Journal on Matrix Analysis and Applications
Volume	26
Issue number	2
DOIs	https://doi.org/10.1137/S0895479803433313
State	Published - 2005

Keywords

Connected components
Distance to uncontrollability
Pseudospectrum
Robust control
Trisection

ASJC Scopus subject areas

Analysis

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10.1137/S0895479803433313

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AU - Lewis, A. S.

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AB - We show that 2-norm pseudospectra of m-by-n matrices have no more than 2m(4m-1) connected components. Such bounds are pertinent for computing the distance to uncontrollability of a control system, since this distance is the minimum value of a function whose level sets are pseudospectra. We also discuss algorithms for computing this distance, including a trisection variant of Gu's recent algorithm, and we show how these may be used to locally maximize the distance to uncontrollability for a parameterized system.

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KW - Pseudospectrum

KW - Robust control

KW - Trisection

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Pseudospectral components and the distance to uncontrollability

Abstract

Keywords

ASJC Scopus subject areas

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