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Machel A.N., Wang K. — Qualitative Theory of Dynamical Systems: The Role of Stability Preserving Mappings
Machel A.N., Wang K. — Qualitative Theory of Dynamical Systems: The Role of Stability Preserving Mappings

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Название: Qualitative Theory of Dynamical Systems: The Role of Stability Preserving Mappings

Авторы: Machel A.N., Wang K.

Аннотация:

Illuminates the most important results of the Lyapunov and Lagrange stability theory for a general class of dynamical systems by developing topics in a metric space independantly of equations, inequalities, or inclusions. Applies the general theory to specific classes of equations. Presents new and expanded material on the stability analysis of hybrid dynamical systems and dynamical systems with discontinuous dynamics


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second Edition

Год издания: 2001

Количество страниц: 707

Добавлена в каталог: 14.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C_0$-semigroup      6 75 210
$C_0$-semigroup, contraction      76
$C_0$-semigroup, infinitesimal generator      75
$C_r = C[[-r,0], R^n]$      61 347
$H^l$, $H^l$-norm      93 342—346 396
$H^l)0$      93 339 342—344 396
$H_0 \overset{\Delta}{=} H_0^0$      354 372 380
$\epsilon$-approximate solution      100
$\mathcal{P}$-matrix      674
$\omega$-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 $\beta$      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 $C^k$      85
Boundary of class $C^{\infty}$, 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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