Linear systems over finite fields: modeling, analysis, and synthesis
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English German |
| Published: |
Aachen
Shaker
2004
|
| Series: | Berichte aus der Steuerungs- und Regelungstechnik
Steuerungs- und Regelungstechnik |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Zugl.: Erlangen-Nürnberg, Univ., Diss., 2004 |
| Physical Description: | XII, 150 S. |
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Record in the Search Index
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| adam_text | IMAGE 1
BERICHTE AUS DER STEUERUNGS- UND REGELUNGSTECHNIK
JOHANN REGER
LINEAR SYSTEMS OVER FINITE FIELDS
MODELING, ANALYSIS, AND SYNTHESIS
D 29 (DISS. UNIVERSITAET ERIANGEN-NUEMBERG)
SHAKER VERLAG AACHEN 2004
IMAGE 2
TABLE OF CONTENTS
1 INTRODUCTION 1
1.1 MOTIVATION 1
1.2 CONTRIBUTION OF THIS DISSERTATION 3
1.3 DISSERTATION OVERVIEW 4
2 MATHEMATICAL PRELIMINARIES 5
2.1 FUNDAMENTAL CONCEPTS OF GROUP THEORY 6
2.2 POLYNOMIALS OVER FINITE FIELDS 9
2.3 LINEAR TRANSFORMATIONS AND MATRICES 12
2.3.1 VECTOR SPACES 12
2.3.2 MATRICES 15
2.3.3 INVARIANTS OF MATRICES 20
2.3.4 THE RATIONAL CANONICAL FORM 20
2.4 AN IMAGE DOMAIN FOR FINITE FIELDS 22
2.4.1 THE *-TRANSFORM 22
2.4.2 TABLE OF CORRESPONDENCES 23
3 FINITE STATE AUTOMATA IN THE STATE SPACE 25
3.1 THE RELATION OF BOOLEAN ALGEBRA WITH THE FINITE FIELD F 2 28
3.2 METHODS FOR DETERMINING THE STATE SPACE MODEL 30
3.2.1 THE DISJUNCTIVE NORMAL FORM METHOD 31
3.2.2 THE REED-MUUER GENERATOR MATRIX METHOD 32
3.2.3 DETERMINISTIC STATE SPACE MODEL 33
IMAGE 3
V NI TABLE OF CONTENTS
4 ANALYSIS OF LINEAR SYSTEMS OVER FINITE FIELDS 37
4.1 LINEAR MODULAR SYSTEMS (LMS) 39
4.2 HOMOGENEOUS LMS 40
4.2.1 CYCLIC DYNAMICS 43
4.2.2 NILPOTENT DYNAMICS 62
4.2.3 ARBITRARY DYNAMICS 68
4.3 INHOMOGENEOUS LMS 71
4.3.1 LINEARIZATION BY TRANSLATION 71
4.3.2 NON-LINEARIZABLE PARTS 74
4.3.3 GENERAL INHOMOGENEOUS LMS 78
4.3.4 EXAMPLE 79
5 SYNTHESIS OF LINEAR SYSTEMS OVER FINITE FIELDS 83
5.1 CONTROLLABILITY OF AN LMS 84
5.1.1 CONTROLLABILITY MATRIX AND CONTROLLABILITY INDICES 85
5.1.2 THE CONTROLLABILITY COMPANION FORM 86
5.2 SYNTHESIS IN THE IMAGE DOMAIN 88
5.2.1 LINEAR STATE FEEDBACK AND ITS STRUCTURAL CONSTRAINTS 88
5.2.2 CONTROLLER DESIGN IN THE IMAGE DOMAIN - WHY? 89
5.2.3 THE POLYNOMIAL MATRIX FRACTION OF THE TRANSFER MATRIX 90
5.2.4 SYNTHESIS ALGORITHM 96
5.2.5 EXAMPLE 99
5.2.6 NON-CONTROLLABLE PARTS 102
5.2.7 EXAMPLE 110
6 CONCLUSIONS AND FUTURE WORK 115
6.1 SUMMARY 115
6.2 FUTURE WORK 117
IMAGE 4
IX
APPENDIX 119
A PERMUTATIONS OF A BLOCK MATRIX 119
* THE TRANSFORMATION MATRIX ON RATIONAL CANONICAL FORM 121
* THE JORDAN NORMAL FORM OVER AN EXTENSION FIELD OF F, 123
D GENERAL SOLUTION OF LINEAR SYSTEMS USING SINGULAR INVERSES 131
E RANK DEFICIENCY OF A MATRIX-VALUED POLYNOMIAL FUNCTION 135
F SOLVING THE LINEAR STATE EQUATION IN THE IMAGE DOMAIN 141
G LIST OF PUBLICATIONS 143
REFERENCES 145
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| language | English German |
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| physical | XII, 150 S. |
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| series2 | Berichte aus der Steuerungs- und Regelungstechnik Steuerungs- und Regelungstechnik |
| spelling | Reger, Johann Verfasser aut Linear systems over finite fields modeling, analysis, and synthesis Johann Reger Aachen Shaker 2004 XII, 150 S. txt rdacontent n rdamedia nc rdacarrier Berichte aus der Steuerungs- und Regelungstechnik Steuerungs- und Regelungstechnik Zugl.: Erlangen-Nürnberg, Univ., Diss., 2004 Lineares System (DE-588)4125617-7 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Zustandsraum (DE-588)4132647-7 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Dynamisches System (DE-588)4013396-5 s Zustandsraum (DE-588)4132647-7 s Lineares System (DE-588)4125617-7 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012872517&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Reger, Johann Linear systems over finite fields modeling, analysis, and synthesis Lineares System (DE-588)4125617-7 gnd Dynamisches System (DE-588)4013396-5 gnd Zustandsraum (DE-588)4132647-7 gnd |
| subject_GND | (DE-588)4125617-7 (DE-588)4013396-5 (DE-588)4132647-7 (DE-588)4113937-9 |
| title | Linear systems over finite fields modeling, analysis, and synthesis |
| title_auth | Linear systems over finite fields modeling, analysis, and synthesis |
| title_exact_search | Linear systems over finite fields modeling, analysis, and synthesis |
| title_full | Linear systems over finite fields modeling, analysis, and synthesis Johann Reger |
| title_fullStr | Linear systems over finite fields modeling, analysis, and synthesis Johann Reger |
| title_full_unstemmed | Linear systems over finite fields modeling, analysis, and synthesis Johann Reger |
| title_short | Linear systems over finite fields |
| title_sort | linear systems over finite fields modeling analysis and synthesis |
| title_sub | modeling, analysis, and synthesis |
| topic | Lineares System (DE-588)4125617-7 gnd Dynamisches System (DE-588)4013396-5 gnd Zustandsraum (DE-588)4132647-7 gnd |
| topic_facet | Lineares System Dynamisches System Zustandsraum Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012872517&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT regerjohann linearsystemsoverfinitefieldsmodelinganalysisandsynthesis |