Positive 1D and 2D systems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Springer
2002
|
| Series: | Communications and control engineering
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XI, 431 S. graph. Darst. : 24 cm |
| ISBN: | 1852335084 9781447110972 |
Staff View
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| 245 | 1 | 0 | |a Positive 1D and 2D systems |c Tadeusz Kaczorek |
| 264 | 1 | |a London [u.a.] |b Springer |c 2002 | |
| 300 | |a XI, 431 S. |b graph. Darst. : 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 0 | |a Communications and control engineering | |
| 500 | |a Literaturangaben | ||
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| 650 | 4 | |a Non-negative matrices | |
| 650 | 4 | |a Positive systems | |
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Record in the Search Index
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| adam_text | TADEUSZ KACZOREK POSITIVE 1D AND 2D SYSTEMS WITH41FIGURES SPRINGER
CONTENTS 1. POSITIVE MATRICES AND GRAPHS 1 1.1 GENERALISED PERMUTATION
MATRIX, NONNEGATIVE MATRIX, POSITIVE AND STRICTLY POSITIVE MATRICES 1
1.2 REDUCIBLE AND IRREDUCIBLE MATRICES 3 1.3 THE COLLATZ - WIELANDT
FUNCTION 8 1.4 MAXIMUM EIGENVALUEOFA NONNEGATIVE MATRIX 10 1.5 BOUNDS ON
THE MAXIMAL EIGENVALUE AND EIGENVECTOR OF A POSITIVE MATRIX 13 1.6
DOMINATING POSITIVE MATRICES OF COMPLEX MATRICES 18 1.7 OSCILLATORY AND
PRIMITIVE MATRICES 19 1.8 THE CANONICAL FROBENIUS FORM OF A CYCLIC
MATRIX 23 1.9 METZLER MATRIX 26 L.LOM-MATRICES 27 1.11 TOTALLY
NONNEGATIVE (POSITIVE) MATRICES 30 1.12 GRAPHS OF POSITIVE SYSTEMS 34
1.13 GRAPHS OF REDUCIBLE, IRREDUCIBLE, CYCLIC AND PRIMITIVE SYSTEMS 41
PROBLEMS 45 REFERENCES 49 2. CONTINUOUS-TIME AND DISCRETE-TIME POSITIVE
SYSTEMS 51 2.1 EXTERNALLY POSITIVE SYSTEMS 51 2.1.1 CONTINUOUS-TIME
SYSTEMS 51 2.1.2 DISCRETE-TIME SYSTEM 53 2.2 INTERNALLY POSITIVE SYSTEMS
55 2.2.1 CONTINUOUS-TIME SYSTEMS 55 2.2.2 DISCRETE-TIME SYSTEMS 59 2.3
COMPARTMENTAL SYSTEMS 60 2.3.1 CONTINUOUS-TIME SYSTEMS 60 2.3.2
DISCRETE-TIME SYSTEMS 61 2.4 STABILITY OF POSITIVE SYSTEMS 63 2.4.1
ASYMPTOTIC STABILITY OF CONTINUOUS-TIME SYSTEMS 63 2.4.2 ASYMPTOTIC
STABILITY OF DISCRETE-TIME SYSTEMS 68 2.5 INPUT-OUTPUT STABILITY 72
2.5.1 BIBO STABILITY OF POSITIVE CONTINUOUS-TIME SYSTEMS 72 2.5.2 BIBO
STABILITY OF INTERNALLY POSITIVE DISCRETE-TIME SYSTEMS 76 2.6 WEAKLY
POSITIVE SYSTEMS 79 2.6.1 WEAKLY POSITIVE CONTINUOUS-TIME SYSTEMS 79
2.6.2 EQUIVALENT STANDARD SYSTEMS FOR SINGULAR SYSTEMS 85 2.6.3
REDUCTION OF WEAKLY POSITIVE SYSTEMS TO THEIR STANDARD FORMS 87 2.6.4
WEAKLY POSITIVE DISCRETE-TIME SYSTEMS 92 VIII 2.6.5 REDUCTION OF WEAKLY
POSITIVE SYSTEMS TO STANDARD POSITIVE SYSTEMS 95 2.7 COMPONENTWISE
ASYMPTOTIC STABILITY AND EXPONENTAL STABILITY OF POSITIVE SYSTEMS 97
2.7.1 CONTINUOUS-TIME SYSTEMS 97 2.7.2 DISCRETE-TIME SYSTEMS 101 2.8
EXTERNALLY AND INTERNALLY POSITIVE SINGULAR SYSTEMS 104 2.8.1
CONTINUOUS-TIME SYSTEMS 104 2.8.2 DISCRETE-TIME SYSTEMS 110 2.9
COMPOSITE POSITIVE LINEAR SYSTEMS 115 2.9.1 DISCRETE-TIME SYSTEMS 115
2.9.2 CONTINUOUS-TIME SYSTEMS 117 2.10 EIGENVALUE ASSIGNMENT PROBLEM FOR
POSITIVE LINEAR SYSTEMS 119 2.10.1 PROBLEM FORMULATION 119 2.10.2
PROBLEM SOLUTION 120 2.10.3 POSITIVE SYSTEMS WITH NONNEGATIVE FEEDBACKS
122 PROBLEMS 123 REFERENCES 126 3. REACHABILITY, CONTROLLABILITY AND
OBSERVABILITY OF POSITIVE SYSTEMS 127 3.1 DISCRETE-TIME SYSTEMS 3.1.1
BASIC DEFINITIONS AND CONE OF REACHABLE STATES 127 3.1.2 NECESSARY AND
SUFFICIENT CONDITIONS OF THE REACHABILITY OF POSITIVE SYSTEMS 131 3.1.3
APPLICATION OF GRAPHS TO TESTING THE REACHABILITY OF POSITIVE SYSTEMS
134 3.2 CONTINUOUS-TIME SYSTEMS 136 3.2.1 BASIC DEFINITIONS AND
REACHABILITY CONE 136 3.3. CONTROLLABILITY OF POSITIVE SYSTEMS 139 3.3.1
BASIC DEFINITIONS AND TESTS OF CONTROLLABILITY OF DISCRETE-TIME SYSTEMS
139 3.3.2 BASIC DEFINITIONS AND CONTROLLABILITY TESTS OF CONTINUOUS-TIME
SYSTEMS 142 3.4 MINIMUM ENERGY CONTROL OF POSITIVE SYSTEMS 144 3.4.1
DISCRETE-TIME SYSTEMS 144 3.4.2 CONTINUOUS-TIME SYSTEMS 148 3.5
REACHABILITY AND CONTROLLABILITY OF WEAKLY POSITIVE SYSTEMS WITH STATE
FEEDBACKS 151 3.5.1 REACHABILITY 151 3.5.2 CONTROLLABILITY 155 3.6
OBSERVABILITY OF DISCRETE-TIME POSITIVE SYSTEMS 156 3.6.1 CONE OF
POSITIVE INITIAL CONDITIONS 156 3.6.2 NECESSARY AND SUFFICIENT
CONDITIONS OF OBSERVABILITY 157 3.6.3 DUAL POSITIVE SYSTEMS AND
RELATIONSHIPS BETWEEN REACHABILITY AND OBSERVABILITY 159 3.7
REACHABILITY AND CONTROLLABILITY OF WEAKLY POSITIVE SYSTEMS 161 3.7.1
REACHABILITY 161 IX 3.7.2 CONTROLLABILITY 165 PROBLEMS 166 REFERENCES
170 4. REALISATION PROBLEM OF POSITIVE 1D SYSTEMS 173 4.1 BASIC NOTIONS
AND FORMULATION OF REALISATION PROBLEM 173 4.1.1 STANDARD DISCRETE-TIME
SYSTEMS 173 4.1.2 STANDARD CONTINUOUS-TIME SYSTEMS 174 4.2 EXISTENCE AND
COMPUTATION OF POSITIVE REALISATIONS 175 4.2.1 COMPUTATION OFMATRIX D OF
A GIVEN PROPER RATIONAL MATRIX 175 4.2.2 EXISTENCE AND COMPUTATION OF
POSITIVE REALISATIONS OF DISCRETE-TIME SINGLE-INPUT SINGLE-OUTPUT
SYSTEMS 177 4.2.3 EXISTENCE AND COMPUTATION OF POSITIVE REALISATIONS OF
CONTINUOUS-TIME SINGLE-INPUT SINGLE-OUTPUT SYSTEMS 186 4.2.4 NECESSARY
AND SUFFICIENT CONDITIONS FOR THE EXISTENCE OF REACHABLE POSITIVE
REALISATIONS 189 4.2.5 DETERMINATION OF AN INTERNALLY POSITIVE
ELECTRICAL CIRCUIT FOR A GIVEN INTERNALLY NONPOSITIVE ONE 196 4.3
EXISTENCE AND COMPUTATION OF POSITIVE REALISATIONS OF MULTI-INPUT
MULTI-OUTPUT SYSTEMS 201 4.3.1 DISCRETE-TIME SYSTEMS 201 4.4 EXISTENCE
AND COMPUTATION OF POSITIVE REALISATIONS OF WEAKLY POSITIVE MULTI-INPUT
MULTI-OUTPUT SYSTEMS 211 4.4.1 PROBLEM FORMULATION 211 4.4.2 EXISTENCE
OF WCF POSITIVE REALISATIONS 214 4.4.3 COMPUTATION OF WCF POSITIVE
REALISATIONS 218 4.4.4 COMPUTATION OF POSITIVE REALISATIONS OF COMPLETE
SINGULAR SYSTEMS 219 4.5 POSITIVE REALISATIONS IN CANONICAL FORMS OF
SINGULAR LINEAR 222 4.5.1 PROBLEM FORMULATION 222 4.5.2 METHODS OF
DETERMINATION OF REALISATIONS 224 PROBLEMS 232 REFERENCES 237 5. 2D
MODEIS OF POSITIVE LINEAR SYSTEMS 241 5.1 INTERNALLY POSITIVE ROESSER
MODEL 241 5.2 EXTERNALLY POSITIVE ROESSER MODEL 243 5.3 INTERNALLY
POSITIVE GENERAL MODEL 248 5.4 EXTERNALLY POSITIVE GENERAL MODEL 250 5.5
POSITIVE FORNASINI-MARCHESINI MODEIS AND RELATIONSHIPS BETWEEN MODEIS
251 5.6 POSITIVE MODEIS OFCONTINUOUS-DISCRETE SYSTEMS 254 5.6.1 POSITIVE
GENERAL CONTINUOUS-DISCRETE MODEL 254 5.6.2 POSITIVE
FORNASINI-MARCHESINI TYPE MODEIS OFCONTINUOUS- DISCRETE SYSTEMS 257
5.6.3 POSITIVE ROESSER CONTINUOUS-DISCRETE TYPE MODEL 259 5.6.4
DERIVATION OF SOLUTION TO THE ROESSER CONTINUOUS-DISCRETE MODEL 262 X
5.7 POSITIVE GENERALISED ROESSER MODEL 264 PROBLEMS 269 REFERENCES 272
6. CONTROUABILITY AND MINIMUM ENERGY CONTROL OF POSITIVE 2D SYSTEMS 275
6.1 REACHABILITY, CONTROUABILITY AND OBSERVABILITY OF POSITIVE ROESSER
MODEL 275 6.1.1 REACHABILITY 275 6.1.2 CONTROUABILITY 281 6.1.3
OBSERVABILITY 281 6.2 REACHABILITY, CONTROUABILITY AND OBSERVABILITY OF
THE POSITIVE GENERAL MODEL 283 6.2.1 REACHABILITY 283 6.2.2
CONTROUABILITY 288 6.2.3 OBSERVABILITY 289 6.3 MINIMUM ENERGY CONTROL OF
POSITIVE 2D SYSTEMS 291 6.3.1 POSITIVE ROESSER MODEL 291 6.3.2 POSITIVE
GENERAL MODEL 295 6.4 REACHABILITY AND MINIMUM ENERGY CONTROL OF
POSITIVE 2D CONTINUOUS-DISCRETE SYSTEMS 297 6.4.1 POSITIVE 2D
CONTINUOUS-DISCRETE SYSTEMS 297 6.4.2 POSITIVE 2D CONTINUOUS-DISCRETE
ROESSER MODEL 301 PROBLEMS 304 REFERENCES 306 7. REALISATION PROBLEM FOR
POSITIVE 2D SYSTEMS 311 7.1 FORMULATION OF REALISATION PROBLEM FOR
POSITIVE ROESSER MODEL 311 7.2 EXISTENCE OF POSITIVE REALISATIONS 312
7.2.1 LEMMAS 312 7.2.2 METHODL. 314 7.2.3 METHOD 2. 318 7.2.4METHOD3.
324 7.3 POSITIVE REALISATIONS IN CANONICAL FORM OF THE ROESSER MODEL 328
7.3.1 PROBLEM FORMULATION 328 7.3.2 EXISTENCE AND COMPUTATION OF
POSITIVE REALISATIONS IN THE ROESSER CANONICAL FORM 329 7.4
DETERMINATION OF THE POSITIVE ROESSER MODEL BY THE USE OF STATE
VARIABLES DIAGRAM 332 7.5 DETERMINATION OF A POSITIVE 2D GENERAL MODEL
FOR A GIVEN TRANSFER MATRIX 337 7.6 POSITIVE REALISATION PROBLEM FOR
SINGULAR 2D ROESSER MODEL 340 7.6.2 PROBLEM SOLUTION 343 7.7 CONCLUDING
REMARKS AND OPEN PROBLEMS 359 PROBLEMS 359 REFERENCES 365 XI APPENDIX A
DETERMINANTAL SYLVESTER EQUALITY 367 APPENDIX B COMPUTATION OF
FUNDAMENTAL MATRICES OF LINEAR SYSTEMS 387 APPENDIX C SOLUTIONS OF 2D
LINEAR DISCRETE MODEIS 403 APPENDIX D TRANSFORMATIONS OF MATRICES TO
THEIR CANONICAL FORMS AND LEMMAS FOR 1D SINGULAR SYSTEMS 411 INDEX 429
|
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| dewey-ones | 512 - Algebra |
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| id | DE-604.BV014038603 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:56:33Z |
| institution | BVB |
| isbn | 1852335084 9781447110972 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009613041 |
| oclc_num | 46937668 |
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| owner | DE-703 DE-83 DE-91 DE-BY-TUM |
| owner_facet | DE-703 DE-83 DE-91 DE-BY-TUM |
| physical | XI, 431 S. graph. Darst. : 24 cm |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Springer |
| record_format | marc |
| series2 | Communications and control engineering |
| spelling | Kaczorek, Tadeusz 1932- Verfasser (DE-588)110868889 aut Positive 1D and 2D systems Tadeusz Kaczorek London [u.a.] Springer 2002 XI, 431 S. graph. Darst. : 24 cm txt rdacontent n rdamedia nc rdacarrier Communications and control engineering Literaturangaben Linear systems Non-negative matrices Positive systems Lineares zeitinvariantes System (DE-588)4213494-8 gnd rswk-swf Nichtnegative Matrix (DE-588)4310434-4 gnd rswk-swf Lineares zeitinvariantes System (DE-588)4213494-8 s Nichtnegative Matrix (DE-588)4310434-4 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009613041&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kaczorek, Tadeusz 1932- Positive 1D and 2D systems Linear systems Non-negative matrices Positive systems Lineares zeitinvariantes System (DE-588)4213494-8 gnd Nichtnegative Matrix (DE-588)4310434-4 gnd |
| subject_GND | (DE-588)4213494-8 (DE-588)4310434-4 |
| title | Positive 1D and 2D systems |
| title_auth | Positive 1D and 2D systems |
| title_exact_search | Positive 1D and 2D systems |
| title_full | Positive 1D and 2D systems Tadeusz Kaczorek |
| title_fullStr | Positive 1D and 2D systems Tadeusz Kaczorek |
| title_full_unstemmed | Positive 1D and 2D systems Tadeusz Kaczorek |
| title_short | Positive 1D and 2D systems |
| title_sort | positive 1d and 2d systems |
| topic | Linear systems Non-negative matrices Positive systems Lineares zeitinvariantes System (DE-588)4213494-8 gnd Nichtnegative Matrix (DE-588)4310434-4 gnd |
| topic_facet | Linear systems Non-negative matrices Positive systems Lineares zeitinvariantes System Nichtnegative Matrix |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009613041&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kaczorektadeusz positive1dand2dsystems |