Fast methods for estimating the distance to uncontrollability

M. Gu; E. Mengi; M. L. Overton; J. Xia; J. Zhu

doi:10.1137/05063060X

Fast methods for estimating the distance to uncontrollability

M. Gu, E. Mengi, M. L. Overton, J. Xia, J. Zhu

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

Abstract

The distance to uncontrollability for a linear control system is the distance (in the 2-norm) to the nearest uncontrollable system. We present an algorithm based on methods of Gu and Burke-Lewis-Overton that estimates the distance to uncontrollability to any prescribed accuracy. The new method requires O(n⁴) operations on average, which is an improvement over previous methods which have complexity O(n⁶), where n is the order of the system. Numerical experiments indicate that the new method is reliable in practice.

Original language	English (US)
Pages (from-to)	477-502
Number of pages	26
Journal	SIAM Journal on Matrix Analysis and Applications
Volume	28
Issue number	2
DOIs	https://doi.org/10.1137/05063060X
State	Published - 2006

Keywords

Complex controllability radius
Distance to uncontrollability
Kronecker product
Real eigen-value extraction
Shift-and-invert Arnoldi
Shifted inverse iteration
Sylvester equation
Trisection

ASJC Scopus subject areas

Analysis

Access to Document

10.1137/05063060X

Cite this

@article{202fa78aefb74a61b6dd0d25d79d363d,

title = "Fast methods for estimating the distance to uncontrollability",

abstract = "The distance to uncontrollability for a linear control system is the distance (in the 2-norm) to the nearest uncontrollable system. We present an algorithm based on methods of Gu and Burke-Lewis-Overton that estimates the distance to uncontrollability to any prescribed accuracy. The new method requires O(n4) operations on average, which is an improvement over previous methods which have complexity O(n6), where n is the order of the system. Numerical experiments indicate that the new method is reliable in practice.",

keywords = "Complex controllability radius, Distance to uncontrollability, Kronecker product, Real eigen-value extraction, Shift-and-invert Arnoldi, Shifted inverse iteration, Sylvester equation, Trisection",

author = "M. Gu and E. Mengi and Overton, {M. L.} and J. Xia and J. Zhu",

year = "2006",

doi = "10.1137/05063060X",

language = "English (US)",

volume = "28",

pages = "477--502",

journal = "SIAM Journal on Matrix Analysis and Applications",

issn = "0895-4798",

publisher = "Society for Industrial and Applied Mathematics Publications",

number = "2",

}

TY - JOUR

T1 - Fast methods for estimating the distance to uncontrollability

AU - Gu, M.

AU - Mengi, E.

AU - Overton, M. L.

AU - Xia, J.

AU - Zhu, J.

PY - 2006

Y1 - 2006

N2 - The distance to uncontrollability for a linear control system is the distance (in the 2-norm) to the nearest uncontrollable system. We present an algorithm based on methods of Gu and Burke-Lewis-Overton that estimates the distance to uncontrollability to any prescribed accuracy. The new method requires O(n4) operations on average, which is an improvement over previous methods which have complexity O(n6), where n is the order of the system. Numerical experiments indicate that the new method is reliable in practice.

AB - The distance to uncontrollability for a linear control system is the distance (in the 2-norm) to the nearest uncontrollable system. We present an algorithm based on methods of Gu and Burke-Lewis-Overton that estimates the distance to uncontrollability to any prescribed accuracy. The new method requires O(n4) operations on average, which is an improvement over previous methods which have complexity O(n6), where n is the order of the system. Numerical experiments indicate that the new method is reliable in practice.

KW - Complex controllability radius

KW - Distance to uncontrollability

KW - Kronecker product

KW - Real eigen-value extraction

KW - Shift-and-invert Arnoldi

KW - Shifted inverse iteration

KW - Sylvester equation

KW - Trisection

UR - http://www.scopus.com/inward/record.url?scp=34247349625&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34247349625&partnerID=8YFLogxK

U2 - 10.1137/05063060X

DO - 10.1137/05063060X

M3 - Article

AN - SCOPUS:34247349625

SN - 0895-4798

VL - 28

SP - 477

EP - 502

JO - SIAM Journal on Matrix Analysis and Applications

JF - SIAM Journal on Matrix Analysis and Applications

IS - 2

ER -

Fast methods for estimating the distance to uncontrollability

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this