Document Details

Document Type : Article In Journal 
Document Title :
A NOTE ON CONTROLLABILTY OF LINEAR SYSTEMS
مذكرة عن الأنظمة القابلة للتحكم LINEAR
 
Subject : A NOTE ON CONTROLLABILTY OF LINEAR SYSTEMS 
Document Language : Arabic 
Abstract : Kalman's minimal realization theory involves geometric objects (controllable, unobservable subspaces) which are subject to structural instability. Specifically, arbitrarily small perturbations in a model may cause a change in the dimensions of the associated subspaces. This situation is manifested in computational difficulties which arise in attempts to apply textbook algorithms for computing a minimal realization. Structural instability associated with geometric theories is not unique to control; it arises in the theory of linear equations as well. In this setting, the computational problems have been studied for decades and excellent tools have been developed for coping with the situation. One of the main goals of this paper is to call attention to principal component analysis (Hotelling, 1933), and an algorithm (Golub and Reinsch, 1970) for computing the singular value decompositon of a matrix. Together they form a powerful tool for coping with structural instability in dynamic systems. As developed in this paper, principal component analysis is a technique for analyzing signals. (Singular value decomposition provides the computational machinery.) For this reason, Kalman's minimal realization theory is recast in terms of responses to injected signals. Application of the signal analysis to controllability and observability leads to a coordinate system in which the "internally balanced" model has special properties. For asymptotically stable systems, this yields working approximations ofX_{c}, X_{bar{o}}, the controllable and unobservable subspaces. It is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces. 
ISSN : 0960-0972 
Journal Name : Far East Journal of Applied 
Volume : 13 
Issue Number : 1 
Publishing Year : 1423 AH
2003 AD 
Article Type : Article 
Added Date : Tuesday, March 19, 2013 

Researchers

Researcher Name (Arabic)Researcher Name (English)Researcher TypeDr GradeEmail
سهام جلال الصيادfisherma, Siham JalalInvestigatorDoctorate 

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