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Blomberg H.( ed.) — Algebraic theory for multivariable linear systems, Volume 166
Blomberg H.( ed.) — Algebraic theory for multivariable linear systems, Volume 166



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Название: Algebraic theory for multivariable linear systems, Volume 166

Автор: Blomberg H.( ed.)

Аннотация:

The present book has evolved out of research work done by a great many people in the course of the last two decades. The work of the older of the present authors, HB, started back in the late fifties with a series of lecture notes on control theory. A safe method was sought for the determination of the correct characteristic polynomial for various feedback and other configurations with the aid of the then so popular transfer function technique. The considerations led to the introduction of an "uncancelled" form of the ordinary transfer function, but the result was not encouraging. In fact, it became apparent that there was something seriously wrong with the traditional form of the whole transfer function representation.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1983

Количество страниц: 360

Добавлена в каталог: 19.04.2011

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Предметный указатель
Abstract algebra      13 301 303—320 321—339 340—341
Abstract input-output system      6 50—55
Abstract input-output system, block diagram representation of      51 57
Adder      30 123
Adjacency matrix      59
Algebra      340
algebraic      321
Algebraic equation      25 110 183 239
Anticausality      285
Associate      305
Augmented matrix      15 172 174
Automorphism of groups      304
Automorphism of vector spaces      341
Binary operation      303
Binary operation, associative      303
Binary operation, commutative      303
Block diagram algebra      120
Boolean matrix      58
Cancellation problem      1
Candidate for feedback compensator      34—44 191
Candidate for feedback compensator, satisfactory      35
Candidate for observer      179
Causal input-output relation      275
Causal system      53 73 231 275
Causality      49 52 66 73 284
Causality, generalized      205 209—216 230
Causality, strict      285
Cause-effect relationship      49 50 52 56 59
Characteristic polynomial      23 29 70 185 292
Coefficient list      221 298
Coefficient matrix      221 222
Coefficient matrix, augmented      221 222
Column equivalence      14 311
Comaximal      305 see "Polynomial
Commutative diagram      93 97
Composition of family of difference input-output relations      288
Composition of family of difference input-output relations, causal      289
Composition of family of difference input-output relations, feedback      291
Composition of family of difference input-output relations, input-output relation determined by      288
Composition of family of difference input-output relations, observable      289
Composition of family of difference input-output relations, order of      289
Composition of family of difference input-output relations, parallel      291
Composition of family of difference input-output relations, reconstructible      289
Composition of family of difference input-output relations, regular      289
Composition of family of differential input-output relations      7 82 90 106 110—122 202 243
Composition of family of differential input-output relations, block diagram representation of      10 113
Composition of family of differential input-output relations, controllability aspects of      121—122
Composition of family of differential input-output relations, description of      115
Composition of family of differential input-output relations, equivalent      114 115 118
Composition of family of differential input-output relations, feedback      12 27 184—190
Composition of family of differential input-output relations, input-output equivalent      107 117
Composition of family of differential input-output relations, input-output relation determined by      112—117 250—251
Composition of family of differential input-output relations, observable      24 117 119
Composition of family of differential input-output relations, observable, partially      118—120
Composition of family of differential input-output relations, order of      117
Composition of family of differential input-output relations, parallel      25 123
Composition of family of differential input-output relations, parallel, controllability aspects of      125—126
Composition of family of differential input-output relations, parallel, observable      125
Composition of family of differential input-output relations, parallel, transfer matrix of      126
Composition of family of differential input-output relations, regular      9 114 116 250
Composition of family of differential input-output relations, series      9 11 26 137—143
Composition of family of differential input-output relations, series, controllability aspects of      142—143
Composition of family of differential input-output relations, series, observable      140—143
Composition of family of differential input-output relations, series, transfer matrix of      139
Composition of family of differential input-output relations, series-parallel      141 143—145
Composition of family of differential input-output relations, system determined by      250—259
Composition of family of differential input-output relations, transfer equivalent      120
Composition of family of differential input-output relations, transfer matrix determined by      120 252
Composition of projection and delay operator      296
Composition of projection and differential operator      216—225
Concatenation property      208
Control input      30
Control problem      236 240
Controllability      25 55 100 159 202 236 286
Controllability index      194
Converse relation      89
Coprime      305 see "Polynomial
Decentralized control      45
Decomposition of difference input-output relation      288
Decomposition of difference input-output relation, parallel      290
Decomposition of differential input-output relation      106 118 160—176
Decomposition of differential input-output relation, observable      118
Decomposition of differential input-output relation, parallel      126—133
Decomposition of differential input-output relation, Rosenbrock representation      160—176
Decomposition of differential input-output relation, series      140—145 197
Decomposition of differential input-output relation, series-parallel      141 143—145
Decomposition of differential input-output relation, state-space      160
Decoupling theory      45
Delta function      206 207 343—348
Delta function, Dirac      343
Delta function, Kronecker      309
Denominator      305
Denominator set      306 325
Determinateness      47 56 63—66 71—72
Diagnostics      45
Difference equation, linear time-invariant      271 274 275 282 284
Difference input-output system      see "Difference system"
Difference system      3 271 273 275 293
Difference system, causal      275
Difference system, linear      294
Differential equation, linear time-invariant      5 73 201
Differential input-output system      see "Differential system"
Differential operator      4 75 76
Differential operator, causal      210
Differential system      3 75 79 90 231
Differential system, causal      230
Differential system, controllable      231
Differential system, dimension of      231
Differential system, linear      230
Differential system, proper      232
Differential system, strictly proper      232
Differentiation operator      4
Differentiation operator, generalized      346
Distinguishable by a single input-output pair      55
distribution      see "Generalized function"
Distributive      303
Divide      305
Division algorithm      17 323—325
Divisor      305 see "Polynomial
Divisor, greatest common      19 305
Dynamic system      52 53 64 69—72 90 107 201 230
Electrical network      259
Elementary column operation      18 312
Elementary matrix      15 311
Elementary row operation      14 311
Elimination procedure      9 23 107—110 116 176
Endomorphism of groups      304
Endomorphism of vector spaces      340
Epimorphism of groups      304
Equivalence of matrices      311
Equivalence of matrices, canonical forms for      315
Estimator      3 107
Euclidean algorithm      324—325
Factor set      306
Feedback compensation      27—44 184—199
Feedback compensator      27—44 184—199 292
Feedback compensator, candidate for      34—44 191—199
Feedback compensator, candidate for, satisfactory      35
Feedback composition      12 27—44 184 187 291
Feedback control      2 27 106 107 184
Feedback interconnection      69
Field      13 304
Field of quotients      14 84 210 278 307
Final segment      204 226
first element      99
Fixed point      63
Fourier transform      1 67
Fundamental theorem of algebra      324
Generalized convolution      345
Generalized derivative      206 343
Generalized differentiation operator      206 346
Generalized function, complex-valued      203 205 342—348
Generalized function, complex-valued, piecewise infinitely regularly differentiable      5 76 203 205—210 345—348
Generalized function, complex-valued, piecewise infinitely regularly differentiable, concatenation property of      208
Generalized function, complex-valued, piecewise infinitely regularly differentiable, subspaces of      208
Generalized function, complex-valued, piecewise infinitely regularly differentiable, value at t      206
Generalized function, complex-valued, regular      342
Generalized function, complex-valued, restriction of      348
Generalized function, complex-valued, singular      343
Generator      337
Generator for difference input-output relation      282
Generator for difference input-output relation, anticausal      285
Generator for difference input-output relation, causal      285
Generator for difference input-output relation, input-output equivalent      283
Generator for difference input-output relation, order of      282
Generator for difference input-output relation, proper      285
Generator for difference input-output relation, regular      282
Generator for difference input-output relation, row equivalent      283
Generator for difference input-output relation, strictly causal      285
Generator for difference input-output relation, transfer equivalent      285
Generator for differential input-output relation      6 88 90—94
Generator for differential input-output relation, characteristic polynomial of      23
Generator for differential input-output relation, input-output equivalent      23 79 88 92—94 96 106
Generator for differential input-output relation, order of      6 90
Generator for differential input-output relation, proper      21 95
Generator for differential input-output relation, quotient equivalent      337
Generator for differential input-output relation, regular      6 88 90 91—92
Generator for differential input-output relation, row equivalent      22 92—94 95
Generator for differential input-output relation, strictly proper      22 95
Generator for differential input-output relation, transfer equivalent      88 95—100
Generator, quotient equivalent      337
Generator, transfer equivalent      337
Green's function      215
Group      303
Group, abelian      303 304
Group, additive      303
Group, commutative      303
Group, multiplicative      303
Hierarchical control      45
Ideal, two-sided      305
Ideal, two-sided, principal      305
Identification      23 44
Impulse response function      215
Indeterminate over ring      13 81 84 277 321
Infinitely continuously differentiable complex-valued function      5 76 206 343
Initial condition list      221
Initial condition mapping      217—225 297
Initial condition mapping for polynomial matrix operator      219 220 297
Initial condition mapping for polynomial operator      219 297
Initial segment      78 204 226 275
Input      50
Input set      50
Input signal      6 78
Input, overall      58 62
Input-output equivalence      23 79 88 92—94 107 117 145 161—170 283
Input-output equivalence, canonical form for      88 93—94 104 162 284
Input-output equivalence, complete invariant for      93—94 162
Input-output mapping      50 201
Input-output mapping, causal      52 209 214—216 231
Input-output mapping, parametric      50—52 64 227 230 241 246 247 249 252
Input-output mapping, parametric, equivalent      51
Input-output relation      51 73 201
Input-output relation, difference      275
Input-output relation, difference, causal      275
Input-output relation, difference, characteristic polynomial of      292
Input-output relation, difference, controllable      286
Input-output relation, difference, decomposition of      288
Input-output relation, difference, generation of      274 see
Input-output relation, difference, minimal      286
Input-output relation, difference, order of      282
Input-output relation, difference, reachable      286
Input-output relation, difference, regular      282
Input-output relation, difference, transfer equivalent      286
Input-output relation, differential      5 78 88 89—105
Input-output relation, differential, asymptotically stable      23
Input-output relation, differential, block diagram representation of      111
Input-output relation, differential, characteristic polynomial of      23
Input-output relation, differential, controllable      25 100 121
Input-output relation, differential, decomposition of      118 197
Input-output relation, differential, generation of      78 89 see
Input-output relation, differential, minimal      97 99 129
Input-output relation, differential, order of      6 90
Input-output relation, differential, proper      21 95
Input-output relation, differential, regular      6 88 90—91
Input-output relation, differential, strictly proper      22 95
Input-output relation, differential, transfer equivalent      88 98—100
Input-output relation, internal      9 113
Input-output relation, internal, reduced      147
Input-output relation, internal-overall      8 115
Input-output relation, overall      8 9 112 115
Input-state relation      158
Insensitivity with respect to parameter variations      34—35 44 178 191 258
Integral domain      13 84 304
Integration by parts      225
Integration in generalized sense      225 343
Interconnection constraint      8 57—59 111 113 245
Interconnection matrix      7 57 61 111
Interconnection of family of differential systems      243—269
Interconnection of family of differential systems, determinate      246 250
Interconnection of family of differential systems, equivalent      255 258
Interconnection of family of differential systems, input-output mapping determined by      246—250
Interconnection of family of differential systems, restricted state space      245—246
Interconnection of family of differential systems, stability properties of      258
Interconnection of family of differential systems, system determined by      247—259
Interconnection of family of differential systems, system determined by, dimension of      250
Interconnection of family of differential systems, transfer matrix determined by      247
Interconnection of family of differential systems, unrestricted state space      244—245
Interconnection of family of systems      56—72 110 201
Interconnection of family of systems, block diagram representation of      62
Interconnection of family of systems, determinate      59 63—67 71—72 114
Interconnection of family of systems, indeterminate      66 72
Interconnection of family of systems, input-output mapping determined by      64 65—67 70—72
Interconnection of family of systems, input-output relation determined by      63 65—67 70—72
Interconnection of family of systems, system determined by      62—64 66—67 71—72
Internal system      62 63—64 65—67 247—259
Inverse      303
Irreducible      305
Isomorphism of groups      304
Isomorphism of rings      84
Kernel      304
Laplace transform      67—68 80 94 149 203 216 224—226
Laplace transform, generalized      225 229
Leading coefficient      35 322
Leading term      322
Linear dynamic system      79 204 226—242
Linear dynamic system, finite dimensional      227—242
Linear mapping      307
Linear mappings, algebra of      84 210 340
Linear system      53—55 201
Linear system, dimension of      54
Linear system, finite dimensional      54 73
Linear system, linear description of      54
LIST      308
Matrix difference equation      275 279
Matrix differential equation      13 78 89
Matrix over principal ideal domain      312—320
Matrix over principal ideal domain, determinantal divisor of      314
Matrix over principal ideal domain, diagonal reduction of      314
Matrix over principal ideal domain, greatest common divisor of      316—320
Matrix over principal ideal domain, invariant factor of      314
Matrix over principal ideal domain, least common multiple of      316
Matrix over principal ideal domain, rank of      315
Matrix over principal ideal domain, secondary      313
Matrix over principal ideal domain, secondary row operation on      313
Matrix over principal ideal domain, Smith (canonical) form of      315
Matrix over principal ideal domain, triangular reduction of      313
Matrix over ring      309
Matrix over ring of quotients      318—320
Matrix over ring of quotients, canonical upper triangular form of      334
Matrix over ring of quotients, quotient equivalent      319
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