Implicit linear systems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin u.a.
Springer
1991
|
| Series: | Lecture notes in control and information sciences
152 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 163 - 172 |
| Physical Description: | XI, 176 S. graph. Darst. |
| ISBN: | 3540535373 0387535373 |
Staff View
MARC
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| 100 | 1 | |a Aplevich, J. Dwight |d 1943- |e Verfasser |0 (DE-588)174104642 |4 aut | |
| 245 | 1 | 0 | |a Implicit linear systems |c J. D. Aplevich |
| 264 | 1 | |a Berlin u.a. |b Springer |c 1991 | |
| 300 | |a XI, 176 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in control and information sciences |v 152 | |
| 500 | |a Literaturverz. S. 163 - 172 | ||
| 650 | 0 | 7 | |a Implizite Definition |0 (DE-588)4161418-5 |2 gnd |9 rswk-swf |
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| 650 | 0 | 7 | |a Lineares System |0 (DE-588)4125617-7 |2 gnd |9 rswk-swf |
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Record in the Search Index
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Contents
1 System models 1
1.1 Motivation for implicit equations 2
1.1.1 Unification 2
1.1.2 Generality 2
Improper systems 2
Constrained inputs 2
Constrained auxiliary variables 3
Under determined and over determined systems 3
Uncertainties 3
1.1.3 Large scale systems 3
1.1.4 Simplicity 4
1.1.5 Non oriented systems 4
1.2 Realizations 5
1.2.1 State space models 5
1.2.2 Polynomial matrix fraction models 5
1.2.3 Rational matrices 7
Algebraic operations 7
Column realizations 10
Row realizations 11
1.3 Dual systems and realizations 12
1.4 Realization from input output data 13
1.5 Notes and references 14
1.6 Further study 14
2 The Kronecker form 19
2.1 Transformation to Kronecker form 19
2.1.1 Blocks of the form Lfi 20
2.1.2 Blocks of the form l\ 21
2.1.3 Blocks of the form I \J6i(0) 21
2.1.4 Blocks of the form J7i(A;) XI 22
2.1.5 Minimal systems 22
2.2 Notes and references 22
2.3 Further study 23
viii CONTENTS
3 Analysis of singularities 25
3.1 Poles and zeros 25
3.1.1 The Kronecker form 26
3.1.2 Non singular pencils 26
3.1.3 Minimal systems 27
3.2 Characteristic gains and frequencies 28
3.3 Gain and frequency matrices and pencils 30
3.3.1 Pole pencils 30
3.3.2 Zero pencils 32
3.3.3 The closed loop system 32
3.3.4 Gain operators 33
3.4 Computation of poles and zeros 33
3.5 Notes and references 34
3.6 Further study 34
4 Systems of minimal dimension 37
4.1 System equivalence and minimality 38
4.1.1 The effect of initial conditions 39
4.2 Conditions for minimality 41
4.2.1 Property 1 42
4.2.2 A concrete subspace sequence 43
4.2.3 Property 2 45
4.2.4 Property 3 47
4.2.5 Property 4 49
4.2.6 Proof of minimality theorem 4.1 50
4.3 The permuted state space form 51
4.3.1 The structure of non minimal systems 51
4.4 A minimization algorithm 54
4.4.1 A small example 56
4.5 An alternative construction 60
4.5.1 An example 61
4.6 Notes and references 64
4.7 Further study 65
5 Canonical representations 67
5.1 Invariance, completeness, and independence 67
5.2 The case n = 0 68
5.3 Column canonical forms 69
5.3.1 Transformation Tl 69
5.3.2 System parameterization 71
5.3.3 An example in Tl form , 72
5.3.4 Direct computation of Tl 72
5.3.5 The block companion form 73
5.3.6 Transformation T2 73
CONTENTS ix
5.3.7 An example of T2 74
5.3.8 Transformation T3 75
5.3.9 An example of T3 75
5.3.10 The minimization example (continued) 75
5.3.11 An alternative transformation 76
5.3.12 Alternative transformation example 77
5.3.13 Parameter locations from T3 78
5.3.14 Canonical polynomial forms 79
Example canonical polynomial form 79
5.4 Other canonical forms 79
5.5 Notes and references 79
5.6 Further study 80
6 Algebraic design applications 83
6.1 Combination of subsystems 84
6.1.1 Direct sum 84
6.1.2 Intersection 84
6.1.3 Permutation 85
Inverse systems 85
6.1.4 Projection 85
6.1.5 Reduction 86
6.2 The algebraic design problem 86
6.2.1 Generalized design equations 87
Observer example 88
6.2.2 The subspace inclusion requirement 89
6.3 Solution parameterization 90
Case 1 91
Case 2 92
Case 3 93
Observer example (continued) 94
6.4 Standard design configurations 94
6.4.1 Exact model matching 94
6.4.2 Feedback compensation with internal stability 96
6.5 Parametric design considerations 97
6.5.1 Row and column permutation 98
6.5.2 Cart and stick example 98
6.5.3 The closed loop reduced system 100
6.5.4 Effective solution 102
6.5.5 Recursive design 102
A recursive structure 103
6.5.6 Numerical considerations 104
6.6 Pole and zero placement 104
6.6.1 Stable factorization 104
6.6.2 Pole placement 106
x CONTENTS
6.6.3 Zero placement 107
Root locus design 107
6.6.4 Placement of finite zeros 109
Effective zero placement 110
Solution of effective zero placement 112
The partition of y 113
Excess inputs 113
Zero placement example 114
Summary 115
6.7 Notes and references 115
6.8 Further study 116
7 Optimization with quadratic cost 119
7.1 Optimization in continuous time 119
7.1.1 The state space form 121
7.1.2 The optimal cost 122
7.1.3 Closed loop solution 122
7.2 Discrete time optimization 124
7.2.1 Discrete time state space systems 125
Relation to continuous time optimization 126
7.3 Filtering 127
7.4 Notes and references 129
7.5 Further study 129
8 System identification 131
8.1 System parameterization 131
8.2 Realization from input output data (continued) 133
8.2.1 Sufficient excitation 135
8.2.2 Implementation 136
The effect of initial values 136
Finite memory 137
8.2.3 Approximate solution and structural parameter selection 137
8.3 Estimation of parameters 139
8.3.1 Estimation of covariances 140
8.4 Notes and references 141
8.5 Further study 141
9 Large scale systems 143
9.1 Solution of operating points 144
9.2 Integration methods 145
9.2.1 Stiffness 146
9.2.2 Implicit equations 147
9.2.3 Higher order methods 148
9.2.4 Vector equations 149
CONTENTS xi
9.3 The Nyquist stability test for large systems 150
9.4 Continuation methods 151
9.5 Notes and references 153
9.6 Further study 154
10 Extensions 155
10.1 Multi operator systems 155
10.2 Realizations 156
10.2.1 Binary operations 156
Realization of scalars 156
General multi rational systems 157
10.3 Equivalence and minimality 158
10.4 Time varying systems 159
10.5 Notes and references 160
10.6 Further study 160 |
| any_adam_object | 1 |
| author | Aplevich, J. Dwight 1943- |
| author_GND | (DE-588)174104642 |
| author_facet | Aplevich, J. Dwight 1943- |
| author_role | aut |
| author_sort | Aplevich, J. Dwight 1943- |
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| building | Verbundindex |
| bvnumber | BV004514924 |
| classification_rvk | SI 845 |
| classification_tum | MAT 344f |
| ctrlnum | (OCoLC)246644951 (DE-599)BVBBV004514924 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV004514924 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T05:16:16Z |
| institution | BVB |
| isbn | 3540535373 0387535373 |
| language | English |
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| physical | XI, 176 S. graph. Darst. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in control and information sciences |
| series2 | Lecture notes in control and information sciences |
| spelling | Aplevich, J. Dwight 1943- Verfasser (DE-588)174104642 aut Implicit linear systems J. D. Aplevich Berlin u.a. Springer 1991 XI, 176 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in control and information sciences 152 Literaturverz. S. 163 - 172 Implizite Definition (DE-588)4161418-5 gnd rswk-swf Lineares dynamisches System (DE-588)4167727-4 gnd rswk-swf Lineares System (DE-588)4125617-7 gnd rswk-swf Lineares System (DE-588)4125617-7 s DE-604 Lineares dynamisches System (DE-588)4167727-4 s Implizite Definition (DE-588)4161418-5 s Lecture notes in control and information sciences 152 (DE-604)BV005848579 152 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002781581&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Aplevich, J. Dwight 1943- Implicit linear systems Lecture notes in control and information sciences Implizite Definition (DE-588)4161418-5 gnd Lineares dynamisches System (DE-588)4167727-4 gnd Lineares System (DE-588)4125617-7 gnd |
| subject_GND | (DE-588)4161418-5 (DE-588)4167727-4 (DE-588)4125617-7 |
| title | Implicit linear systems |
| title_auth | Implicit linear systems |
| title_exact_search | Implicit linear systems |
| title_full | Implicit linear systems J. D. Aplevich |
| title_fullStr | Implicit linear systems J. D. Aplevich |
| title_full_unstemmed | Implicit linear systems J. D. Aplevich |
| title_short | Implicit linear systems |
| title_sort | implicit linear systems |
| topic | Implizite Definition (DE-588)4161418-5 gnd Lineares dynamisches System (DE-588)4167727-4 gnd Lineares System (DE-588)4125617-7 gnd |
| topic_facet | Implizite Definition Lineares dynamisches System Lineares System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002781581&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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