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Luenberger D.G. Ч Introduction to dynamic systems
Luenberger D.G. Ч Introduction to dynamic systems

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Ќазвание: Introduction to dynamic systems

јвтор: Luenberger D.G.

јннотаци€:

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.


язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1979

 оличество страниц: 446

ƒобавлена в каталог: 08.12.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
Absorbing state      237
Accessibility      235 246
Adjoint equation      398Ч399 400 406Ч407 411 417 418
Albinism      391
Algebraic multiplicity      85
Alleles      383
Allocation problem      418Ч419 422Ч423
Amortization      22Ч23
angular momentum      389
Arms races      206Ч211 221 222Ч223
Arrow Ч McManus theorem      380
Asymptotic stability      154Ч155 322
Asymptotic stability in large      339 350
bacteria      357Ч358 363
Barter      390Ч391
Basis vectors      70 72 75Ч76
Beats      45Ч47
Bellman      424 435
Blackjack      251 253
Book rotations      74Ч75
Brachistrochrone      429Ч430 435
Bricks      368Ч370
Cable car      8Ч9
Calculus of variations      396 435
Canonical form for linear systems      289Ч296 313 315
Canonical form for Markov chain      239
Canonical form, Jordan      85Ч86 89
Catenary      430
Chain letter      21Ч22
Champernowne model      251Ч253
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      235Ч239
Closed classes      237
Closed-loop control      296Ч297
Cobweb model      23Ч26 54 163Ч164 183
Coefficients      16 39 56 92 93
Cofactor      62Ч63 66
Cohort population model      5Ч6 95Ч96 170Ч174 184Ч185 197
Communicating states      235 246
Companion matrix      96 289Ч290
Comparative statics      211Ч215 221 223
Competitive economy      378Ч382 390 391Ч392
Competitive exclusion      328Ч331
Complex roots      33 36 79
Constant coefficients      16 32Ч38 92 115 132
Constant of motion      328 377
Constraint      395 405
Continuous time      2
Control      94 254Ч255 296 393 395
Controllability      276Ч285 315
Controllability canonical form      290Ч293
Coordinate vectors      70
Cramer's rule      66
Cultural system      105Ч108 152Ч154 167Ч170
Delay      98 269
Determinant      62Ч66
Diagonal matrix      57
Diagonalization      81Ч82 136Ч142
Diagrams      3 97Ч99 142
Difference equation      2 14Ч37
Difference equation, linear      16 26Ч37 261Ч263
Differential equation      38
Differential equation, linear      39 40Ч44 273Ч274
Differential equation, numerical solution      51Ч52
Discrete time      2
Discrete time, optimal control      416Ч419 421Ч423
Distinct roots      33 43 80Ч82 264
Dominant eigenvalues      165Ч170 191 195Ч196 206
dot notation      91
Dot product      59
Duopoly      180Ч181 187
Dynamic diagrams      97Ч99 142
Dynamic phenomena and systems, i      3
Dynamic programming      419Ч425 434 435
Ecological Liapunov function      372
Economics, duopoly      180Ч181
Economics, equilibria      378Ч382 390 391Ч392
Economics, national      6Ч8 122Ч123 131 220Ч221 432Ч433
Economics, supply-demand      23Ч26 48Ч49
Ehrenfest diffusion model      248
Eigenvalue      77 135Ч150
Eigenvalue placement theorem      299Ч300
Eigenvalue, dominant      165Ч170
Eigenvalue, Frobenius Ч Perron      194
Eigenvalues and stability      154Ч159
Eigenvector      77 135Ч150
Embedded statics      121Ч123 130 222
Energy      332 343 354 365Ч367
entropy      249 253 367Ч370
Epidemics      376Ч378 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      17Ч19 40
Exponential growth      8
Exponential matrix      116 140Ч141
Extent of stability      338Ч339
Eye color      384Ч385
Feedback      270Ч272 296Ч300 315 415Ч416
Fibonacci sequence      34Ч35 48
Finite escape time      318Ч319
Fish harvesting      432
Fitness      331 385Ч389
Floquet theory      129
Free system      99Ч100
Free terminal time      409Ч413
Frobenius Ч Perron eigenvalue      194
Frobenius Ч Perron theorem      189 191Ч192 193 222 230Ч231
Fundamental lemma      68Ч69
Fundamental matrix      102
Fundamental matrix of Markov chain      239Ч240
Fundamental solutions      28Ч30 42 101Ч104 113 114
Gambler's ruin      36Ч38 50Ч54 226Ч227 236Ч237 243Ч245
Genetics      17 324 382Ч389 392
Geodesics      429
Geometric growth      4Ч5
Geometric multiplicity      85
Geometric ramp      260 261
Geometric sequences      32 133Ч134
Goats and wolves      10 370
groups      215Ч217
Hamilton Ч Jacobi Ч Bellman equation      424 434 435
Hamiltonian      396 417 429
Hardy Ч Weinberg proportions      383Ч384
Harmonic motion      44Ч47 117
Harrod model      122
Hawkins Ч Simon conditions      223
hierarchies      199Ч204 219
Hog cycle      162Ч165 183Ч184 186
Homans Ч Simon model      215Ч217 222 223
Homogeneous equation      26Ч31 41 68Ч69
Homogeneous system      99 113
Housing      433
Identity matrix      57
Impulse response      111Ч112 119Ч121 267Ч268
Infinite Markov chains      245Ч248 253
Information theory      49 54 253
Initial conditions      17Ч18 39 91
Inner product      59
Inputs      93Ч94 254Ч255
Insects      403Ч405 435
Integrator      99 275
Interest      22 47
Invariant set      345
Inverse      66Ч68 197Ч198
Irreducible      236 246 250
Isoperimetric problem      408Ч409
Jacobian      326
Jordan canonical form      85Ч86 89
Kepler's laws      367
Kermac and McKendrick      376 391
Krasovskii's method      362
Lagrange multipliers      431
Lanchester model      117Ч118 128 131
Languages      248
Laplace transform      272Ч276 314
Laplace's expansion      62Ч64 86 87
Lattice vibrations      185Ч186 187
Learning model      226 229 236 241 253
Left eigenvector      83 142Ч147
Leontief model      61Ч62 89 218
Liapunov functions      319 332Ч339 347Ч354 364 366 368 372 374 375 382 386 427
Liapunov's first method      325Ч328
Liapunov's second method      332Ч339
Limit cycle      345Ч347
Linear algebraic equations      56
Linear difference equation      16 26Ч40
Linear differential equation      39 40Ч44
Linear independence of eigenvectors      79Ч80
Linear independence of functions      42
Linear independence of sequences      30Ч31
Linear independence of vector      71
Linear independence of vector functions      114
Linear independence of vector sequences      101
Linear Liapunov function      347Ч349
Linear system      92 132
Linear-quadratic problem      413Ч416 425 432
Linearization      127Ч128 324Ч328
logistic      317Ч318 321 324 356 373
Lotka      370Ч391
Lure      363
Marginal stability      157Ч159 322
Markov chain      225
Matrix      56
Maximum principle      394 400 407 411
McPhee's model      152Ч154 186
Metzier matrix      204Ч206 222 390
Migration model      144Ч147 179Ч180 186
Minor, of elements of matrix      62
Modal matrix      81 137 180
Modified objective      396Ч398 406 410Ч411 417
Monopoly game      232Ч234 253
Multiple eigenvalues      84Ч86 148Ч150
Natchez Indians      105Ч108 131 174Ч178 180 186
Newton cooling      53
Newton's Laws      8Ч9 97 365Ч367
Nonhomogeneous equation      26Ч27 31Ч32 41
Nonhomogeneous system      108Ч112 118Ч121 196Ч199
Nonlinear systems      125 127 316Ч363
Nonnegative matrix      190Ч191 193
Objective      393 395
Observability      285Ч289 315
Observability canonical forms      293Ч295
observers      300Ч309 314 315
Optimal control      393Ч435
Optimal return function      420Ч421
Order      15Ч16 38 90
Orthogonality      84
oscillations      160Ч165
Outputs      254Ч255
Pareto's law      252
Partial fractions      263Ч266 309Ч310
Pendulum      341Ч343 346Ч347 366
Periodic Markov chain      246 251
Permutation matrix      249 250
Perron      189 222
Peter Principle      199Ч204 219 222
Planetary motion      367 389
Pontryagin      394 435
Population      5Ч6 10 144Ч147 170Ч174 184Ч185 186 370Ч375
Positive definite      351Ч352
Positive eigenvalue      172 191Ч195
Positive matrix      190Ч191 249Ч250
Positive recurrent chain      247Ч248
Positive system      188 195Ч199 204Ч206 347Ч349 355Ч356
Poverty and wealth      251Ч253
Predator-prey model      10 370Ч375 390
Principle of optimality      419Ч420
Probability vector      227
Production line      241Ч243
Proper rational function      257
Pursuit problem      343Ч345
Pushcart      402Ч403 428
Puzzle      125Ч126 131
Quadratic cost      413Ч416 432
Quadratic form      350Ч353
QUEUE      50
Radioactive dating      53
Random walk      245 247Ч248 250 251
Rank      72
Rational function      257
Reduced order observers      304Ч306 315
Reducible chain      236 249
Regular Markov chain      230
Repeated roots      49 84Ч86 148Ч150 264
Reproductive value      185
Riccati equation      415 425
Richardson's theory      206Ч211 221 222Ч223
Right eigenvector      83 142Ч147
Roulette      36Ч38 50
Routh test      181Ч183 187
Samuelson      123 131
Scalar multiplication      58
Seismograph      53Ч54
Separation theorem      307Ч308
Series expansion of inverse      198 217
Sickle cell anemia      385 391
Similar matrices      88
Simulation      11
Singular matrix      66
Social system      105Ч108 125
Square root algorithm      339Ч341
Stability      154Ч159 322Ч328
Stability and optimal control      425Ч427 434Ч435
Stability of positive systems      190 196Ч197 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      100Ч101
Stick balancing      283Ч285 300 306Ч307 308Ч309 311
Stochastic matrices      227
Straight-through cohort model      94Ч95 99 124
structures      184 187
Subdominant modes      167
Substochastic matrix      239
Summarizing function      319 354Ч356 364
Superposition      109Ч112 119Ч121
Supply and demand      23Ч26 48Ч49
Symmetric matrix      88 352
system      2 90
System eigenvectors      135Ч150
System matrix      92 93
Tatonnement      378Ч382 392
Terminal constraints      405Ч409 431
Thermodynamics      367Ч370 391
Time-invariant      16 92 104 115Ч118 317
Trace      88
Trajectory      323
Transfer function      266Ч267 275 295Ч296
Transformation      73Ч76
transforms      255Ч276 314
Transient class      237 239Ч245
Transition probabilities      225 228
1 2
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