Column-wise relative degree and it’s properties

International Journal of Mathematics and Systems Science

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Field Value
 
Title Column-wise relative degree and it’s properties
 
Creator Kraev, Andrey Vladimirovich
Rogovskiy, A. I.
 
Subject Control theory; linear dynamical systems; relative degree; zero dynamics; canonical forms
 
Description Many questions of control theory are well studied for systems which satisfy to the relative degree definition. If this definition is fulfilled then there exists linear state-space transform reducing system to a very convenient canonical form where zero dynamics is a part of system’s equations. Algorithms of such reduction are well-known. However, there exist systems which don’t satisfy this definition. Such systems are the subject of investigation in the presented paper. To investigate their properties here we suggest to consider an analogue of the classical relative degree definition – the so-called column-wise relative degree. It turned out that this definition is satisfied in some cases when classical relative degree doesn’t exist. We introduce this notion here, investigate it properties and suggest algorithm for reducing systems to the column-wise relative degree compliant form if possible. It is possible to show that systems with column-wise relative degree also can be reduced to a convenient canonical form by a linear state-space transformation. Some problems arise from the fact that some systems which do not have relative degree can be reduced to a form with it using linear inputs or outputs transform. Here we show that this is an interesting mathematical problem, which can be solved with the help of properties of relative degree, formulated and proved in this paper.
 
Publisher EnPress Publisher LLC
 
Contributor
 
Date 2018-11-02
 
Type info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Peer-reviewed Article
 
Format application/pdf
 
Identifier https://systems.enpress-publisher.com/index.php/IJMSS/article/view/675
10.24294/ijmss.v1i4.675
 
Source International Journal of Mathematics and Systems Science; Vol 1, No 4 (In publishing)
2578-1839
10.24294/ijmss.v1i4
 
Language eng
 
Relation https://systems.enpress-publisher.com/index.php/IJMSS/article/view/675/765
https://systems.enpress-publisher.com/index.php/IJMSS/article/downloadSuppFile/675/214
 
Rights Copyright (c) 2018 International Journal of Mathematics and Systems Science
http://creativecommons.org/licenses/by-nc/4.0
 

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