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Machel A.N., Wang K. — Qualitative Theory of Dynamical Systems: The Role of Stability Preserving Mappings |
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Предметный указатель |
-semigroup 6 75 210
-semigroup, contraction 76
-semigroup, infinitesimal generator 75
61 347
, -norm 93 342—346 396
93 339 342—344 396
354 372 380
-approximate solution 100
-matrix 674
-limit set 22 209 414
Absolute stability 288 289 437
Abstract time 28
Aizerman's conjecture 289
Allowed event trajectory 225
Artificial neural network 295 319
Artificial neural network with time delay 382 439
Ascoli —Arzela Lemma 99 314
Associative memory 659 675
Asymptotic properties 118 470
Asymptotic stability see asymptotically stable
Asymptotic stability in the large see asymptotically stable
Asymptotically stable 9 10 12—14 16 17 19 20 22 23 32—35
Asymptotically stable in the large see asymptotically stable
Asymptotically stable, finite dynamical system 265 268 271 272 280 282—285 287 302—304 310 316—318
Asymptotically stable, general dynamical system 118 120—122 129 141 145 153 154 158 168—171 178 180 182 183 185 186 190—192 199 208 213 214 227 233 236 239 243 246 247 251
Asymptotically stable, hybrid and discontinuous dynamical system 470—473 502 512 514—516 520 522 523 526 531 539 542 548 557—562 566 613 624 626 665—667 672
Asymptotically stable, infinite dimensional dynamical system 340 343 348 361 363—365 368 369 373 374 380 392—395 400—402 406 416 417 425
Asynchronous solution 658
Atomic at 393
Attractive 9 118 121 122 129 152
Autonomous 151
Autonomous, difference equation 281
Autonomous, differential equation 151 279
Autonomous, differential inclusion 206 420 421
Autonomous, system 21 206
Basic sample step 500 598
Basic sampling period 467
Bit, byte 238
Boundary 43
Boundary condition 89
Boundary of class 85
Boundary of class , smooth boundary 85 88
Bounded motion 44 119
Bounded solution 49 see uniformly
buffers 229
Cauchy — Kovalevskaya Theorem 91 104
Chetaev's instability theorem 277
Chetaev's instability theorem for differential equation in Banach space 395
Chetaev's instability theorem for functional differential equation 357
Class K 11 127
Class KL 153
Class KR 11 127
Class L 152
Class W 519
Compact imbedding 360
Companion matrix 52
Comparison system 13 134 222 284
Comparison system, difference equation as comparison system 181 316 317
Comparison system, difference inequality as comparison system 60 61 169 243
Comparison system, differential equation as comparison system 173 284 285 367
Comparison system, differential inequality as comparison system 59 167 171
Comparison system, functional differential equation as comparison system 402
Comparison system, parabolic partial differential equation as comparison system 370
Comparison theorem for continuous-time general dynamical system 168 178 179
Comparison theorem for discrete-time general dynamical system 169 182
Comparison theorem for functional differential equation 402
Comparison theorem for general dynamical system 135
Comparison theorem for ordinary difference equation 316 317
Comparison theorem for ordinary differential equation 284 285
Comparison theorem for ordinary differential equation in Banach space 367
Comparison theorem for partial differential equation 373
Comparison theorem, comparison theory 13 111 125 512
Complete instability 9 14 34 35 136 137 138 172 244 286 287 317 see
completely continuous 65 363
Completely unstable 14 16 137 141 145 158 159 172 173 194 244 245 249 274 287 313 317 318 352 353 532 534 see
Composite system 403 565 see
Composition (of motions) 197 541
Computer network balancing problem 25 234
Concatenation 225
Conservative dynamical system 53 267
Continuable forward for all time 45
Continuation 44 48 65
Continuous imbedding 360 361
Continuous load 235
Continuous semigroup 210
Continuous set-valued mapping 415
Continuous time dynamical system 4 538
Continuous-time dynamics 463
Controllable 291
Converse theorem 540
Converse theorem for asymptotic stability 250
Converse theorem for exponential stability 203 283 325 366
Converse theorem for stability 250
Converse theorem for uniform asymptotic stability 199 283
Converse theorem for uniform stability 197 282
Convex Frechet space 403
Convex hull 415
Critical case 602
d'Alembert's formula 104
DDS see discontinuous dynamical system
Decentralized system 376 see
Decomposable 376
Decrescent 263 309 336
Diagonally dominant matrix 667
Diagonally stable 670
Differential equation in Banach space 7 79 334 411
Differential inclusion in Banach space 7 79 334
Differential-difference equation 62 67 341 350 356 358 363
Digital controller 464
Dini derivative 42 43
Direct control problem 289 439
Direct method (of Lyapunov) 125 221
Discontinuous dynamical system 29 459 476 490 510 611
Discrete event 457
Discrete event system 8 24 44 95 224
Discrete job 230
Discrete load 235
Discrete semigroup 210
Discrete time 457
Discrete time dynamical system 4 538 539
Discrete-time dynamics 463
Dissipative 76
Domain of attraction 9 118 273 472
Dynamical system 3 4 43 44 60 67
Elliptic operator 369 see also strongly elliptic
Embedding 360 474 475
Enable function 224
Energy function 24 220 652 683
Energy function, (local) minimum of 653 683
Engine-drive train system 465
Equicontinuous 99
Equilibrium 9 10 114 178 182 260 335 401 469 473 558 650
EQUIVALENCE 10 126 511
Equivalent (qualitative property) 10 31 126 511
Equivalent time space 461
Event 224
Event trajectory 224 225
Evolution in time forward 112
Exponential stability see exponentially stable
Exponential stability in the large see exponentially stable
Exponential stability preserving mapping 12 32 33 127 264 515
Exponentially stable 10 12 13 14 16 17 19 20 32—35
Exponentially stable in the large see exponentially stable
Exponentially stable, finite dimensional dynamical system 265 268 271 272 283 285 287 311 315—318
Exponentially stable, general dynamical system 119—122 132 141 145 154 158 159 168—171 178 180 182 183 185 187 190—192 203 242 243 246 251
Exponentially stable, hybrid and discontinuous dynamical system 471—473 503 512 514 515 520 522 528 531 539 546 552 557—562 565 566 568 570 572 586 587 602
Exponentially stable, infinite dimensional dynamical system 340 343 344 366 368 373 374 379 380 390 399 401 402 425 428 430 431 433
Extension 48
Extreme system 426
Fading memory space 159 338
| Family of motions 44
Finite dimensional dynamical system 4 259 482
First order ordinary difference equation 55
First order ordinary differential equation 45
Fixed point 47 64
Fixed-point digital filter 301
Fixed-point quantization 322 609
Floating-point quantization 322
Functional differential equation of the neutral type 6 66
Functional differential equation of the retarded type 5 61 62 337
General dynamical system 240 see also dynamical system
General hybrid dynamical system 458 460
General system 44 see also dynamical system
Generalized distance function 24 220
Generalized energy function 220
Generalized potential force 53
Generalized time 28 474 458 470
Global exponential stability see exponentially stable
Global uniform asymptotic stability see asymptotically stable
Globally asymptotically stable see asymptotically stable
Gronwall inequality 100
Hamiltonian system 53 267 275 277
HDS see hybrid dynamical system
Heat equation 103 123 344
Hille — Yoshida — Phillips theorem 76
Hybrid dynamical system 8 28 29 95 98 375 376 380 462 463
Hybrid dynamical system, defined on R+ 460 481
Imbedding see embedding
Incidence matrix 253
Indirect control 291 439
Infinite dimensional dynamical system 5 333
Infinite sector condition 450
Infinite wordlength 600
Initial condition 44 see also initial value problem
Initial time 4 44
Initial value problem 46 55 56 59 63 66 67 413
Instability 14 34 35 136 138 243 see
Interconnected system 376 403 565
Interconnecting structure 403 569
Interface elements 463
Invariance 13 17 32 127 168 169 180 183 190 512 557 559 560
Invariance principle, finite dimensional dynamical system 279 281
Invariance principle, infinite dimensional dynamical system 359 360 363
Invariance principle, invariance theorem, invariance theory 22 279 405 418
Invariance principle, semigroup 210—214
Invariant (set) 8 9 12 20 34 35 112 117 127 171 181 186 190—192 227 243 260 261 405 406 421 469 473 520 523 539
Kamke function see class K class class
kinetic energy 53
Lagrange equation 14 54
Lagrange stability 120
Lienard equation 280
Lifted column vector 500 599
Lifted state space representation 500 501 599 600
Limit cycle 301
Linear complementarity system 639 660
Linear differential-difference equation of the neutral type 67
Linear differential-difference equation of the retarded type 63
Linear homogeneous ordinary, differential equation 50 51 102
Linear operator, closed 75
Linear operator, dissipative 76
Linear operator, spectral set, spectrum 75
Linear parabolic equation 88 338 342 344
Linear sampled-data feedback control systems 685
Linear semigroup 6 75
Linear systems with state saturation constraints 660 687
Linear time invariant ordinary differential equation 14 140
Linear Volterra integrodifferential equation 6 71 159
Linearization 144 516 599 601
Lipschitz condition 48 64 217
Local solution 677 678
Locally compact 23 214
Lower semicontinuous 415
Lure's result 288 290
Lyapunov function 24 220
Lyapunov matrix equation 14 140 157
Lyapunov's first instability theorem for differential equation in Banach space 352
Lyapunov's first instability theorem for functional differential equation 355
Lyapunov's first instability theorem for general motions 193 248
Lyapunov's first instability theorem for ordinary difference equation 312
Lyapunov's first instability theorem for ordinary differential equation 274
Lyapunov's first method 15 145 158
Lyapunov's second instability theorem for differential equation in Banach space 353
Lyapunov's second instability theorem for general motions 195 249
Lyapunov's second instability theorem for ordinary difference equation 313
Lyapunov's second instability theorem for ordinary differential equation 276
Lyapunov's second method see direct method (of Lyapunov)
M-matrix 181 246
Manufacturing system 25
Maximal principle 103
Maximal solution 176 400
Minimal solution 176
Modified Nyquist plot 294
Monotone increasing 558
Monotone nondecreasing 19 182
Motion 4 43 226 461 462 538
Motion control 465
Multi-modal system 483
Multi-rate digital feedback control system 467 499 597 686
Multi-rate sampled-data feedback control system 686
Multi-rate sampler 500
Multi-rate zero-order-hold element 468 500
n-th order ordinary difference equation 56
n-th order ordinary differential equation 51 52
Nagumo — Westphal lemma 370
Negative (semi) trajectory 117
Negative definite (function) 262 308 336
Negative invariant set 112
Negative semidefinite 262 336
Neighborhood (of a set) 191
Neural network 295 319 638 675
Neutral functional differential equation 66 see functional differential equation of the neutral type
Non-smooth dynamical system 459
Noncontinuable 45 48 65 177
Nonlinear parabolic equation 338 370
Nonlinear semigroup 6 77
Null event 224
Object of inquiry 13 134 222
Observable 323
Orbital stability 228
Ordinary difference inequality 60 115 169
Ordinary differential equations 115
Ordinary differential equations in Banach space 116
Ordinary differential inequalty 3 58 167
Output bin 229
output sequence 655
Output vector 651
Parabolic equation 86 92 369
Partial differential equation 3 147 338
Partial motion 197 541
Partial state saturation constraints 492 660 671
Peano — Cauchy existence theorem 48
Period, periodic 117
Petri net 24 224 253
Plant 464 467
Poincare's inequality 148 345 353 381
Poisson's formula 104 124
Popov criterion 291 292
Popov plot 294
Position control system 496
Positive (semi) trajectory 117 414
Positive definite (function) 262 308 336
Positive invariant set 112
Positive semidefinite 262 336
potential energy 53
Principal Lyapunov stability results 19 33 185 519
producer 229
Proper (with respect to) 137
Pulse width modulated feedback control system 487 610 686
Quadratic Lyapunov function 667
Qualitative equivalence 9 111
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