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Luenberger D.G. — Introduction to dynamic systems

Luenberger D.G. — Introduction to dynamic systems

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Название: Introduction to dynamic systems

Автор: Luenberger D.G.

Аннотация:

This book is an outgrowth of a course developed at Stanford University over the past five years. It is suitable as a self-contained textbook for second-level undergraduates or for first-level graduate students in almost every field that employs quantitative methods. As prerequisites, it is assumed that the student may have had a first course in differential equations and a first course in linear algebra or matrix analysis. These two subjects, however, are reviewed in Chapters 2 and 3, insofar as they are required for later developments. The objective of the book, simply stated, is to help one develop the ability to analyze real dynamic phenomena and dynamic systems.
This objective is pursued through the presentation of three important aspects of dynamic systems: (1) the theory, which explores properties of mathematical representations of dynamic systems, (2) example models, which demonstrate how concrete situations can be translated into appropriate mathematical representations, and (3) applications, which illustrate the kinds of questions that might be posed in a given situation, and how theory can help resolve these questions. Although the highest priority is, appropriately, given to the orderly presentation of the theory, significant samples of all three of these essential ingredients are contained in the book.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1979

Количество страниц: 446

Добавлена в каталог: 08.12.2005

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Предметный указатель

Absorbing state      237
Accessibility      235 246
Adjoint equation      398—399 400 406—407 411 417 418
Albinism      391
Algebraic multiplicity      85
Alleles      383
Allocation problem      418—419 422—423
Amortization      22—23
Arms races      206—211 221 222—223
Arrow — McManus theorem      380
Asymptotic stability      154—155 322
Asymptotic stability in large      339 350
bacteria      357—358 363
Barter      390—391
Basis vectors      70 72 75—76
Beats      45—47
Bellman      424 435
Blackjack      251 253
Book rotations      74—75
Brachistrochrone      429—430 435
Bricks      368—370
Cable car      8—9
Calculus of variations      396 435
Canonical form for linear systems      289—296 313 315
Canonical form for Markov chain      239
Canonical form, Jordan      85—86 89
Catenary      430
Chain letter      21—22
Champernowne model      251—253
Characteristic equation for difference equations      32
Characteristic equation for differential equations      43
Characteristic equation for matrices      77
Characteristic polynomial      33 43 77
Classes of states      235—239
Closed classes      237
Closed-loop control      296—297
Cobweb model      23—26 54 163—164 183
Coefficients      16 39 56 92 93
Cofactor      62—63 66
Cohort population model      5—6 95—96 170—174 184—185 197
Communicating states      235 246
Companion matrix      96 289—290
Comparative statics      211—215 221 223
Competitive economy      378—382 390 391—392
Competitive exclusion      328—331
Complex roots      33 36 79
Constant coefficients      16 32—38 92 115 132
Constant of motion      328 377
Constraint      395 405
Continuous time      2
Control      94 254—255 296 393 395
Controllability      276—285 315
Controllability canonical form      290—293
Coordinate vectors      70
Cramer's rule      66
Cultural system      105—108 152—154 167—170
Delay      98 269
Determinant      62—66
Diagonal matrix      57
Diagonalization      81—82 136—142
Diagrams      3 97—99 142
Difference equation      2 14—37
Difference equation, linear      16 26—37 261—263
Differential equation      38
Differential equation, linear      39 40—44 273—274
Differential equation, numerical solution      51—52
Discrete time      2
Discrete time, optimal control      416—419 421—423
Distinct roots      33 43 80—82 264
Dominant eigenvalues      165—170 191 195—196 206
dot notation      91
Dot product      59
Duopoly      180—181 187
Dynamic diagrams      97—99 142
Dynamic phenomena and systems, i      3
Dynamic programming      419—425 434 435
Ecological Liapunov function      372
Economics, duopoly      180—181
Economics, equilibria      378—382 390 391—392
Economics, national      6—8 122—123 131 220—221 432—433
Economics, supply-demand      23—26 48—49
Ehrenfest diffusion model      248
Eigenvalue      77 135—150
Eigenvalue placement theorem      299—300
Eigenvalue, dominant      165—170
Eigenvalue, Frobenius — Perron      194
Eigenvalues and stability      154—159
Eigenvector      77 135—150
Embedded statics      121—123 130 222
Energy      332 343 354 365—367
entropy      249 253 367—370
Epidemics      376—378 390 391
Equi-dimensional equation      53
Equilibrium point      150 320
Equilibrium point of positive system      190 196 206
Equivalence classes      249
Escape velocity      389
Estate planning      430 434
Existence and uniqueness      17—19 40
Exponential growth      8
Exponential matrix      116 140—141
Extent of stability      338—339
Eye color      384—385
Feedback      270—272 296—300 315 415—416
Fibonacci sequence      34—35 48
Finite escape time      318—319
Fish harvesting      432
Fitness      331 385—389
Floquet theory      129
Free system      99—100
Free terminal time      409—413
Frobenius — Perron eigenvalue      194
Frobenius — Perron theorem      189 191—192 193 222 230—231
Fundamental lemma      68—69
Fundamental matrix      102
Fundamental matrix of Markov chain      239—240
Fundamental solutions      28—30 42 101—104 113 114
Gambler's ruin      36—38 50—54 226—227 236—237 243—245
Genetics      17 324 382—389 392
Geodesics      429
Geometric growth      4—5
Geometric multiplicity      85
Geometric ramp      260 261
Geometric sequences      32 133—134
Goats and wolves      10 370
groups      215—217
Hamilton — Jacobi — Bellman equation      424 434 435
Hamiltonian      396 417 429
Hardy — Weinberg proportions      383—384
Harmonic motion      44—47 117
Harrod model      122
Hawkins — Simon conditions      223
hierarchies      199—204 219
Hog cycle      162—165 183—184 186
Homans — Simon model      215—217 222 223
Homogeneous equation      26—31 41 68—69
Homogeneous system      99 113
Housing      433
Identity matrix      57
Impulse response      111—112 119—121 267—268
Infinite Markov chains      245—248 253
Information theory      49 54 253
Initial conditions      17—18 39 91
Inner product      59
Inputs      93—94 254—255
Insects      403—405 435
Integrator      99 275
Interest      22 47
Invariant set      345
Inverse      66—68 197—198

Irreducible      236 246 250
Isoperimetric problem      408—409
Jacobian      326
Jordan canonical form      85—86 89
Kepler's laws      367
Kermac and McKendrick      376 391
Krasovskii's method      362
Lagrange multipliers      431
Lanchester model      117—118 128 131
Languages      248
Laplace transform      272—276 314
Laplace's expansion      62—64 86 87
Lattice vibrations      185—186 187
Learning model      226 229 236 241 253
Left eigenvector      83 142—147
Leontief model      61—62 89 218
Liapunov functions      319 332—339 347—354 364 366 368 372 374 375 382 386 427
Liapunov's first method      325—328
Liapunov's second method      332—339
Limit cycle      345—347
Linear algebraic equations      56
Linear difference equation      16 26—40
Linear differential equation      39 40—44
Linear independence of eigenvectors      79—80
Linear independence of functions      42
Linear independence of sequences      30—31
Linear independence of vector      71
Linear independence of vector functions      114
Linear independence of vector sequences      101
Linear Liapunov function      347—349
Linear system      92 132
Linear-quadratic problem      413—416 425 432
Linearization      127—128 324—328
logistic      317—318 321 324 356 373
Lotka      370—391
Lure      363
Marginal stability      157—159 322
Markov chain      225
Matrix      56
Maximum principle      394 400 407 411
McPhee's model      152—154 186
Metzier matrix      204—206 222 390
Migration model      144—147 179—180 186
Minor, of elements of matrix      62
Modal matrix      81 137 180
Modified objective      396—398 406 410—411 417
Monopoly game      232—234 253
Multiple eigenvalues      84—86 148—150
Natchez Indians      105—108 131 174—178 180 186
Newton cooling      53
Newton's Laws      8—9 97 365—367
Nonhomogeneous equation      26—27 31—32 41
Nonhomogeneous system      108—112 118—121 196—199
Nonlinear systems      125 127 316—363
Nonnegative matrix      190—191 193
Objective      393 395
Observability      285—289 315
Observability canonical forms      293—295
observers      300—309 314 315
Optimal control      393—435
Optimal return function      420—421
Order      15—16 38 90
Orthogonality      84
oscillations      160—165
Outputs      254—255
Pareto's law      252
Partial fractions      263—266 309—310
Pendulum      341—343 346—347 366
Periodic Markov chain      246 251
Permutation matrix      249 250
Perron      189 222
Peter Principle      199—204 219 222
Planetary motion      367 389
Pontryagin      394 435
Population      5—6 10 144—147 170—174 184—185 186 370—375
Positive definite      351—352
Positive eigenvalue      172 191—195
Positive matrix      190—191 249—250
Positive recurrent chain      247—248
Positive system      188 195—199 204—206 347—349 355—356
Poverty and wealth      251—253
Predator-prey model      10 370—375 390
Principle of optimality      419—420
Probability vector      227
Production line      241—243
Proper rational function      257
Pursuit problem      343—345
Pushcart      402—403 428
Puzzle      125—126 131
Quadratic cost      413—416 432
Quadratic form      350—353
QUEUE      50
Radioactive dating      53
Random walk      245 247—248 250 251
Rank      72
Rational function      257
Reduced order observers      304—306 315
Reducible chain      236 249
Regular Markov chain      230
Repeated roots      49 84—86 148—150 264
Reproductive value      185
Riccati equation      415 425
Richardson's theory      206—211 221 222—223
Right eigenvector      83 142—147
Roulette      36—38 50
Routh test      181—183 187
Samuelson      123 131
Scalar multiplication      58
Seismograph      53—54
Separation theorem      307—308
Series expansion of inverse      198 217
Sickle cell anemia      385 391
Similar matrices      88
Simulation      11
Singular matrix      66
Social system      105—108 125
Square root algorithm      339—341
Stability      154—159 322—328
Stability and optimal control      425—427 434—435
Stability of positive systems      190 196—197 206 222
State of Markov chain      225
state variables      91 92 93
State vector      95 317
State-transition matrix      100 113 126 138 140
State-transition property      100—101
Stick balancing      283—285 300 306—307 308—309 311
Stochastic matrices      227
Straight-through cohort model      94—95 99 124
structures      184 187
Subdominant modes      167
Substochastic matrix      239
Summarizing function      319 354—356 364
Superposition      109—112 119—121
Supply and demand      23—26 48—49
Symmetric matrix      88 352
system      2 90
System eigenvectors      135—150
System matrix      92 93
Tatonnement      378—382 392
Terminal constraints      405—409 431
Thermodynamics      367—370 391
Time-invariant      16 92 104 115—118 317
Trace      88
Trajectory      323
Transfer function      266—267 275 295—296
Transformation      73—76
transforms      255—276 314
Transient class      237 239—245
Transition probabilities      225 228
TRANSPOSE      60 64

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