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Staffans O. — Well-Posed Linear Systems
Staffans O. — Well-Posed Linear Systems



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Название: Well-Posed Linear Systems

Автор: Staffans O.

Язык: en

Рубрика: Математика/Математическая Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 871

Добавлена в каталог: 25.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Dilation      25
Dilation of a semigroup      702
Dilation of a system      715
Dilation of system      25
Dilation, co-isometric      702—714
Dilation, isometric      702—714
Dilation, minimal      702
Dilation, unitary      702—714
dim(X)      xiv
Direct sum      196
Discrete time      60 762—769
Dissipative operator      119—123
Doubly coprime factorization      19
Dual      15
Dual generators      370 374
Dual of closed-loop system      470
Dual of flow-inverted system      395—396
Dual of LP      130
Dual of partially flow-inverted system      429—430
Dual system      364—376
Duality between observation and control      602—613
Dynamic controller      19
Dynamic stabilization      19 497 532 533 535 536
Eigenvalue      xv 102 112
Eigenvector      xv 102 112
Energy preserving extension      715—720
Energy preserving system      24 686—693
Exactly controllable      564—573
Exactly controllable in finite time      607
Exactly observable      564—573
Exactly observable in finite time      608
Exponential shift      55
Exponential stability      18
Extended system      488
Extrapolation space      10
Factorization of Hankel operator      559—563
Factorization, doubly coprime      503
Factorization, doubly coprime, joint      503
Feedback      17
Feedback cancellation      447 448
Feedback partial      451
Feedback partial, compatible      472
Feedback partial, identity      452 453
Feedback, compatible      467—468
Feedback, dynamic output      450 451 523
Feedback, regular      468—474
Feedback, state      454 455 491
Feedback, static output      433—449
Feedback, static output, cancellation      441
Feedback, static output, repeated      441
Feedthrough operator      4 12 13 26 32 223 236 240—247 342 762
Feedthrough operator, determined by control operator      302 303
Fefferman's theorem      661
Final space      803
Final time      41 362
Final time, $+\infty$      41
Final time, $-\infty$      362
Flow-inversion      16 376—396 598
Flow-inversion compatible      389—391
Flow-inversion of system node      381
Flow-inversion, dual      395—396
Flow-inversion, partial      599
Flow-inversion, regular      391—395
Flow-invertible      16 379 380 386—388 406 766
Flow-invertible, dual      395 429
Flow-invertible, operator node      383 411
Flow-invertible, partially      418 425—427
Flow-invertible, system node      388
Forcing function      11
Forward wave operator      81
Fraction coprime, left      502
Fraction coprime, right      502
Fractional order      161
Fractional power      154—163 173 207
Frequency domain      1 184—191
Functional calculus      154—163
Gamma function      xvi 162 319
Gamma function, reflection formula      162
Generator of $C_{0}$ group      93
Generator of $C_{0}$ semigroup      93 96—106 116 118
Generator of $C_{0}$ semigroup on a Hilbert space      179 180 634
Generator of analytic semigroup      166 169 172
Generator of bounded semigroup      118
Generator of co-isometric semigroup      690
Generator of contraction semigroup      119—121
Generator of diagonal semigroup      112
Generator of dual semigroup      127
Generator of isometric semigroup      690
Generator of Lax-Phillips model      279 665
Generator of normal semigroup      115
Generator of shift semigroup      98—100 107 110 207
Generator of shift semigroup, frequency domain description      193
Generator of uniformly continuous group      94
Generator of unitary semigroup      690
Generator, bounded      94 95
Generator, closed      96
Generator, closed-loop      458—470
Generator, dual      370
Gram operator      578 752
Gramian controllability      22 569 570 635—643
Gramian observability      22 569 570 635—643
Group      39
Group analytic      94
Group shift      90
Group, $C_{0}$      39
Group, locally bounded      39
Group, strongly continuous      39
Growth bound      9 65—72 90
Hankel operator      20 73 75 76 88 550 609 614
Hankel operator factorization      559—563
Hankel operator of inverse      377
Hankel operator, closed range      545 608 609
Hankel, realization      559—563
Hautus rank conditions      495 588—590
Heaviside function      xvi 346
Hille — Yosida theorem      116—119
Hyperbolic      88
Hyperbolic partial differential equation      86 207 208
Identity feedback, negative      440
Identity feedback, positive      440
Incoming subspace      78
Induced input normalized system      574
Induced output normalized system      574
Initial space      803
Initial state      41 70 360
Initial time      31 41 223 360 362
Initial time, $-\infty$      70 71 257 259
INNER      24
Inner state space      78
Input function      32 41 360
input map      8 38 41 212
Input map, backward      360 362
Input normalized      20
Input sensitivity      439
Input space      1 38
Input, complementary sensitivity      439
Input, loop gain      438
Input, return difference      439
Input/output map      1 8 38 41 75 76
Input/output map, backward      360 362
Input/output map, regular      342—354
Interaction operator      488
Internal loop      543
Interpolation space      10 161
Intertwined semigroups      205
Invariant      715
Invariant subspace      11 196—205 548
Invariant, co-invariant      715
Inversion flow      376—396
Inversion time      396—406
Inversion, partial flow      415—430
Inversion, time-flow      406—414
Isometric      680
Isometric dilation      702
Isometric operator      803
Isometric semigroup      662
Isometry      803
Isometry, partial      803
j      xiii
Jointly, admissible      21
Jointly, stabilizable and detectable      19
Kalman — Yakubovich — Popov inequality      759
Laguerre series      775
Laguerre shift      779
Laguerre transform      28 775—787
Laplace transform      1 11 184—191 252 254 628 810 812
Laplace transform finite      184
Laplace transform, $L^{2}$-version in Hilbert space      630 634
Laplace transform, bilateral      184
Laplace transform, left-sided      184 286 288
Lax—Phillips model      71 78—84 89—91 279 281
Lax—Phillips model, dual      369
Lax—Phillips model, inverse      409
Lebesgue extension      356
Lebesgue point      336 337 339 341 356
Left invertible      602
Linear fractional transform      27 770—774
Local degree      589
LOG      xvi
Loop break point      437
Loop gain      438
lossless      24 740
Lossless system      694—701
Lyapunov equation controllability      22 637
Lyapunov equation observability      22 635
Lyapunov equation, residual      636 637
Main operator      3 13 26 262 762
Matrix of an operator      641
McMillan degree      589
Meromorphic      589
Minimal dilation      25
Minimal losses      758
Minimal realization      20 545—552 554
Minimal system      546
Modal, controllability      21 593—595
Modal, minimality      593
Modal, observability      21 593—595
Mode, controllable      593
Mode, observable      593
Negative norm      10
Nilpotent      590
Node      2 37
Normal generator      115
Normal operator      114 203
Normal semigroup      115 283 287 288 644 654
Normal system      13 287—289 651
Normalized realization      574—582
Null space of adjoint      603
Numerator      502
Observability approximate      20
Observability exact      564—573
Observability of transformed system      598—601
Observability, conditions      583—592
Observability, gramian      21 22
Observable      20 546
Observable mode      593—595
Observable subspace of Lax — Phillips model      721
Observation operator      4 12 26 233—239 263 762
Observation operator, $L^{\infty}$-well-posed      234
Observation operator, bounded      12 31 50 86 223 243 244 248 350
Observation operator, closable      306
Observation operator, compatible extension      300
Observation operator, dense range      291
Observation operator, dual      370
Observation operator, extended      300 326—337
Observation operator, Reg-well-posed      234
Observation/feedthrough operator      248—277 297
Observation/feedthrough operator, closed-loop      458
Observation/feedthrough operator, extended      338—341
Operator node      13 261
Operator node, compatible extension      302
Operator node, extended      302
Operator, closed      124
Operator, densely defined      126
Operator, dual, xiv      124 125
Operator, sectorial      164—177
Optimal system      747
Optimal, *-optimal system      747
Order of a pole      589
Orthonormal basis      110 111 136 207 283 284 641
Outgoing subspace      78
Output function      32 41 71
Output function, backward      360
Output injection      17 454—457 599
Output map      8 38 41 212
Output map, backward      360 362
Output normalized      20
Output sensitivity      439
Output space      1 38
Output, complementary sensitivity      439
Output, feedback      433—453 599
Output, feedback operator      434 442 443
Output, loop gain      438
Output, of system node      267
Paley — Wiener      630
Parabolic      88 164
Parabolic partial differential equation      86 207 208
Parallel connection      13 58 59 498
Parallel connection, compatible      307
Parallel connection, dual      367
Parbalanced realization      577
Part of an operator in a subspace      204
Partial differential equation hyperbolic      86 207 208
Partial differential equation parabolic      86 207 208
Partial flow-inversion      415—430 448
Partial flow-inversion, compatible      427—428
Partial flow-inversion, dual      429—430
Partial flow-inversion, regular      428—429
Partial isometry      803
passive      23
Passive realization      740—754
Passive system      673—685
Passive system node      673—685
Passive, purely      681
Pivot space      138
Pole      589
Positive norm      10
Positive operator      802
Potapov — Ginzburg transformation      17
Power stable      768
pre-annihilator      586
Pritchard — Salamon class      87
Projection      196
Projection of X onto Z along Y      196
Pseudo-similar      20
Pseudo-similar realizations      553—558
Purely contractive      24 681
Purely passive      24 684
Purely passive part of input/output map      684
Quotient map      231 547
Quotient semigroup      549
Quotient space      547
Range of adjoint      603
Range, closed      603
Rank(A)      xiv
Reachable subspace      546
Reachable subspace of Lax — Phillips model      721
Realization      20 74 76 77 87 217 512 545 614
Realization *-restricted shift      615
Realization compatible      309
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