On D-stability and structured singular values

Jie Chen; Michael K.H Fan; Cheng-Ching Yu

doi:10.1016/0167-6911(94)00036-U

Researcher login

CityU Scholars

A Research Hub of Excellence

System upgrade will be carried out on 12 Dec 2024 (THU) from 8:00 pm to 9:00 pm (HK Time). The system will not be available during this period.

On D-stability and structured singular values

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

Overview

13 Scopus Citations

Scopus Metrics

View graph of relations

Author(s)

Jie Chen
Michael K.H Fan
Cheng-Ching Yu

Detail(s)

Original language	English
Pages (from-to)	19-24
Journal / Publication	Systems and Control Letters
Volume	24
Issue number	1
Publication status	Published - 9 Jan 1995
Externally published	Yes

Link(s)

DOI	DOI https://doi.org/10.1016/0167-6911(94)00036-U Final Published version
	Check@CityULib
Link to Scopus	https://www.scopus.com/record/display.uri?eid=2-s2.0-0029639919&origin=recordpage
Permanent Link	https://scholars.cityu.edu.hk/en/publications/publication(34a69ac5-a70a-4786-93ec-5c6e3b20d7d8).html

Abstract

It is shown in this paper that there are close connections between the notion of D-stability of a real square matrix and several quantities related to the structured singular value. As a main result, we show that a real square matrix is D-stable if and only if the real structured singular value of some complex matrix is less than one. This condition implies that checking D-stability may in general be an NP-hard problem. Since the exact verification of D-stability is difficult, we provide several additional conditions that are either necessary or sufficient, and these conditions are also connected to the real or complex structured singular values. These results are further extended to the notion of strong D-stability. © 1995.