Equivalence of rational representations of behaviors
This article deals with the equivalence of representations of behaviors of linear differential systems. In general, the behavior of a given linear differential system has many different representations. In this paper we restrict ourselves to kernel and image representations. Two kernel representatio...
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| Veröffentlicht in: | Systems & control letters 2011-02, Vol.60 (2), p.119-127 |
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| creator | Gottimukkala, Sasanka V. Fiaz, Shaik Trentelman, Harry L. |
| description | This article deals with the equivalence of representations of behaviors of linear differential systems. In general, the behavior of a given linear differential system has many different representations. In this paper we restrict ourselves to kernel and image representations. Two kernel representations are called equivalent if they represent one and the same behavior. For kernel representations defined by polynomial matrices, necessary and sufficient conditions for equivalence are well known. In this paper, we deal with the equivalence of rational representations, i. e. kernel and image representations that are defined in terms of rational matrices. As the first main result of this paper, we will derive a new condition for the equivalence of rational kernel representations of possibly noncontrollable behaviors. Secondly we will derive conditions for the equivalence of rational representations of a given behavior in terms of the polynomial modules generated by the rows of the rational matrices. We will also establish conditions for the equivalence of rational image representations. Finally, we will derive conditions under which a given rational kernel representation is equivalent to a given rational image representation. |
| doi_str_mv | 10.1016/j.sysconle.2010.11.003 |
| format | Article |
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In general, the behavior of a given linear differential system has many different representations. In this paper we restrict ourselves to kernel and image representations. Two kernel representations are called equivalent if they represent one and the same behavior. For kernel representations defined by polynomial matrices, necessary and sufficient conditions for equivalence are well known. In this paper, we deal with the equivalence of rational representations, i. e. kernel and image representations that are defined in terms of rational matrices. As the first main result of this paper, we will derive a new condition for the equivalence of rational kernel representations of possibly noncontrollable behaviors. Secondly we will derive conditions for the equivalence of rational representations of a given behavior in terms of the polynomial modules generated by the rows of the rational matrices. We will also establish conditions for the equivalence of rational image representations. Finally, we will derive conditions under which a given rational kernel representation is equivalent to a given rational image representation.</description><identifier>ISSN: 0167-6911</identifier><identifier>EISSN: 1872-7956</identifier><identifier>DOI: 10.1016/j.sysconle.2010.11.003</identifier><identifier>CODEN: SCLEDC</identifier><language>eng</language><publisher>Amsterdam: Elsevier B.V</publisher><subject>[formula omitted]-modules ; Applied sciences ; Behaviors ; Computer science; control theory; systems ; Control system analysis ; Control systems ; Control theory. 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In general, the behavior of a given linear differential system has many different representations. In this paper we restrict ourselves to kernel and image representations. Two kernel representations are called equivalent if they represent one and the same behavior. For kernel representations defined by polynomial matrices, necessary and sufficient conditions for equivalence are well known. In this paper, we deal with the equivalence of rational representations, i. e. kernel and image representations that are defined in terms of rational matrices. As the first main result of this paper, we will derive a new condition for the equivalence of rational kernel representations of possibly noncontrollable behaviors. Secondly we will derive conditions for the equivalence of rational representations of a given behavior in terms of the polynomial modules generated by the rows of the rational matrices. We will also establish conditions for the equivalence of rational image representations. Finally, we will derive conditions under which a given rational kernel representation is equivalent to a given rational image representation.</description><subject>[formula omitted]-modules</subject><subject>Applied sciences</subject><subject>Behaviors</subject><subject>Computer science; control theory; systems</subject><subject>Control system analysis</subject><subject>Control systems</subject><subject>Control theory. Systems</subject><subject>Equivalence</subject><subject>Exact sciences and technology</subject><subject>Kernels</subject><subject>Mathematical analysis</subject><subject>Matrices</subject><subject>Matrix methods</subject><subject>Rational annihilators</subject><subject>Rational kernel and image representations</subject><subject>Representations</subject><issn>0167-6911</issn><issn>1872-7956</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><recordid>eNqFkM1OwzAQhC0EEqXwCqgXxCnBazuJcwNV5UeqxKV3y3HWwlWatN60Ut-ehBaunFaandnRfozdA0-BQ_60TulIrmsbTAUfRUg5lxdsAroQSVFm-SWbDMYiyUuAa3ZDtOacCy7lhKnFbh8OtsHW4azzs2j70LW2mUXcRiRs-x-Bxl2FX_YQuki37MrbhvDuPKds9bpYzd-T5efbx_xlmTglRJ-AqARoAQ4E1JjXZWU9So41aGfLykPmXVXUXCultOQKOM_AO5_lstRWyyl7PJ3dxm63R-rNJpDDprEtdnsyOlcKxJidsvzkdLEjiujNNoaNjUcD3IyQzNr8QjIjJANgBkhD8OFcYcnZxkfbukB_aSG1lIUeC55PPhzePQSMhlwYmdUhoutN3YX_qr4Bng6Ang</recordid><startdate>20110201</startdate><enddate>20110201</enddate><creator>Gottimukkala, Sasanka V.</creator><creator>Fiaz, Shaik</creator><creator>Trentelman, Harry L.</creator><general>Elsevier B.V</general><general>Elsevier</general><scope>6I.</scope><scope>AAFTH</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SP</scope><scope>7TA</scope><scope>8FD</scope><scope>JG9</scope><scope>L7M</scope></search><sort><creationdate>20110201</creationdate><title>Equivalence of rational representations of behaviors</title><author>Gottimukkala, Sasanka V. ; Fiaz, Shaik ; Trentelman, Harry L.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c422t-12b21821c121de6d9bafe30ed18ca9bf15fcb7d08444830410051fcf56398a83</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>[formula omitted]-modules</topic><topic>Applied sciences</topic><topic>Behaviors</topic><topic>Computer science; control theory; systems</topic><topic>Control system analysis</topic><topic>Control systems</topic><topic>Control theory. Systems</topic><topic>Equivalence</topic><topic>Exact sciences and technology</topic><topic>Kernels</topic><topic>Mathematical analysis</topic><topic>Matrices</topic><topic>Matrix methods</topic><topic>Rational annihilators</topic><topic>Rational kernel and image representations</topic><topic>Representations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Gottimukkala, Sasanka V.</creatorcontrib><creatorcontrib>Fiaz, Shaik</creatorcontrib><creatorcontrib>Trentelman, Harry L.</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Electronics & Communications Abstracts</collection><collection>Materials Business File</collection><collection>Technology Research Database</collection><collection>Materials Research Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Systems & control letters</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Gottimukkala, Sasanka V.</au><au>Fiaz, Shaik</au><au>Trentelman, Harry L.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Equivalence of rational representations of behaviors</atitle><jtitle>Systems & control letters</jtitle><date>2011-02-01</date><risdate>2011</risdate><volume>60</volume><issue>2</issue><spage>119</spage><epage>127</epage><pages>119-127</pages><issn>0167-6911</issn><eissn>1872-7956</eissn><coden>SCLEDC</coden><abstract>This article deals with the equivalence of representations of behaviors of linear differential systems. 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| language | eng |
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| source | ScienceDirect Journals (5 years ago - present) |
| subjects | [formula omitted]-modules Applied sciences Behaviors Computer science control theory systems Control system analysis Control systems Control theory. Systems Equivalence Exact sciences and technology Kernels Mathematical analysis Matrices Matrix methods Rational annihilators Rational kernel and image representations Representations |
| title | Equivalence of rational representations of behaviors |
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