NDLI: A restatement of the major principal direction alignment principle for robustness quantification

Content Provider	IEEE Xplore Digital Library
Author	Baab, C.T. Latchman, H.A. Crisalle, O.D.
Copyright Year	2003
Description	Author affiliation: Dept. of Chem. Eng., Florida Univ., Gainesville, FL, USA (Baab, C.T.)
Abstract	The major principal direction alignment (MPDA) principle, developed in the context of robust control theory, states that a necessary and sufficient condition for the spectral radius of a matrix to equal its maximum singular value is that the major input and the major output principal directions of the matrix be aligned. The MPDA principle emerged from a study of the derivatives of the maximum singular value. An ambiguity that occurs when the maximum singular value is repeated is considered in this paper, together with a modified statement of the major principal direction alignment principle. The new necessary and sufficient condition for the spectral radius of a matrix to equal its maximum singular value is that there exists at least one major input and output principal direction pair of the matrix that is aligned. A rigorous proof is provided for the new necessary and sufficient condition, which makes use of early results on dual norms and dual vectors. An example is presented to illustrate the results.
Sponsorship	American Automatic Control Council IFAC
Starting Page	4828
Ending Page	4833
File Size	413677
Page Count	6
File Format	PDF
ISBN	0780378962
ISSN	07431619
DOI	10.1109/ACC.2003.1242487
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2003-06-04
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Robustness Upper bound Uncertainty Chemical engineering Control theory Linear systems Robust control Linear algebra
Content Type	Text
Resource Type	Article
Subject	Electrical and Electronic Engineering

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Stability robustness bounds and robust stability for linear systems with structured uncertainty

Robust decentralized control for fuzzy large-scale systems using dynamic output-feedback

Robust SISO controller order reduction

Sliding mode control with uncertainty adaptation for uncertain input-delay systems

Local robust performance analysis for nonlinear dynamical systems

Robustness for the uncertain systems with guaranteed cost design

Robust guaranteed cost control with H/sub /spl infin//-/spl gamma/ disturbance attenuation performance

A self tuning RISE controller formulation

Robustness analysis of linear parameter varying systems using integral quadratic constraints

A restatement of the major principal direction alignment principle for robustness quantification

Similar Documents

Stability robustness bounds and robust stability for linear systems with structured uncertainty

Robust decentralized control for fuzzy large-scale systems using dynamic output-feedback

Robust SISO controller order reduction

Sliding mode control with uncertainty adaptation for uncertain input-delay systems

Local robust performance analysis for nonlinear dynamical systems

Robustness for the uncertain systems with guaranteed cost design

Robust guaranteed cost control with H/sub /spl infin//-/spl gamma/ disturbance attenuation performance

A self tuning RISE controller formulation

Robustness analysis of linear parameter varying systems using integral quadratic constraints

A restatement of the major principal direction alignment principle for robustness quantification