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| Staffans O. — Well-Posed Linear Systems |
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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,  41
Final time,  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  group 93
Generator of semigroup 93 96—106 116 118
Generator of 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, 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, 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,  -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,  -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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