Machel A.N., Wang K. — Qualitative Theory of Dynamical Systems: The Role of Stability Preserving Mappings :: Электронная библиотека попечительского совета мехмата МГУ

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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

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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

Предметный указатель

Quasimonotone nondecreasing      18 174 558
Radially unbounded      263 308 336
Rayleigh's dissipation function      54
Razumikhin-type theorem      391
Reachable      657
Real Time      457
Regulator system      288 434
Restriction (of system)      190
Retarded functional differential equation      6 61 62
Robust stability      28 426
Sample      463
Sample and hold element      463
Sample multi-rate      500
Sampled-data control system      464 476 585
Schauder's fixed point theorem      64
Sector condition      289 434
Semigroup      6 22 116 210 linear and
Set-valued mapping      413
Simultaneous event      238
Sliding mode      487 648 649
Sobolev space      85
Sobolev space, solution      46 55 58 403 414 483 648
Sobolev's imbedding theorem      360
Solution in the sense of Filippov      484 486
Solution of (GE)      335
Stability      see stable
Stability preserving mapping      2 9 10 24 31 33 111 125 126 511 515
Stable      9 10 13 17 19 20 32 34 35
Stable operator      394
Stable output vector      651
Stable, finite dimensional dynamical system      265 271 284 310 316
Stable, general dynamical system      118 121 122 129 152 168 169 178 180—183 185 186 190—192 197 207 226 232 238 241—243 250
Stable, hybrid and discontinuous dynamical system      470 473 476 512 502 520 523 539 541 557—560 562 566 568
Stable, infinite dimensional dynamical system      340 343 347 365 368 373 391 394 401 402 405 416 417 425 428 430
State saturation constraints      492 659
State trajectory      225
Strongly stability preserving mapping      11 12 32 33 126 127 511 515
Subsystem      44
Switched system      483 574
Switching rule      483
System defined on a closed hypercube      492 659
System of differential inclusion      27 413

System plant      500
System with impulse effects      482
System with variable structure      see variable structure system
Task      229
Time space      460
Trajectory      117 210
Transfer function      292
Trigger function      465
Undecomposable (system)      376
Uniform asymptotic stability      see asymptotically stable
Uniform asymptotic stability in the large      see asymptotically stable
Uniform boundedness      see uniformly bounded
Uniform global asymptotic stability      see asymptotically stable
Uniform stability      see stable
Uniform ultimate boundedness      see uniformly ultimately bounded
Uniformly asymptotically stable      see asymptotically stable
Uniformly asymptotically stable in the large      see asymptotically stable
Uniformly attractive      9 119 121 153
Uniformly bounded      10 12 14 17 19 20 33—35 99
Uniformly bounded, finite dimensional dynamical system      269 272 285 317
Uniformly bounded, general dynamical system      119 121 122 131 169 170 179 180 182 184 186 253 254
Uniformly bounded, hybrid and discontinuous dynamical system      471 473 503 514 515 522 535 537 553 557—559 561
Uniformly bounded, infinite dimensional dynamical system      345 346 348 373 394 398 400—402
Uniformly stable      see stable
Uniformly ultimately bounded      10 12 14 17 19 20 33—35
Uniformly ultimately bounded, finite dimensional dynamical system      270 273 285 317
Uniformly ultimately bounded, general dynamical system      119 121 122 169 170 179 180 182 184 187 254
Uniformly ultimately bounded, hybrid and discontinuous dynamical system      471 473 503 514 515 522 535 537 554 557—559 561 593 594 627
Uniformly ultimately bounded, infinite dimensional dynamical system      346 348 373 400—402
Uniqueness property      23 24 114 216
Unstable      9 14—16 34 35
Unstable output vector      651
Unstable, finite dimensional dynamical system      274 276 277 282 312 313
Unstable, general dynamical system      119 121 122 136 138 139 141 145 158 159 172 173 194 195 205 243—245 248 249
Unstable, hybrid and discontinuous dynamical system      471 474 503 532—534 587 590 602 607
Unstable, infinite dimensional dynamical system      352—355 357 359 363 396
Upper semicontinuous      415
Valid event trajectory      224 225
Variable structure system      483 484 638 687
Vector Lyapunov function      221 555
Volterra integro differential equation      6 71 148 159 338
Wave equation      87 104
Yacubovich — Kalman Lemma      291

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