Introduction to Dynamic Systems: Theory, Models, and Applications

✍ Scribed by David G. Luenberger

• Publisher: Wiley
• Year: 1979
• Tongue: English
• Leaves: 460
• Edition: 1
• Category: Library

✦ Synopsis

Integrates the traditional approach to differential equations with the modern systems and control theoretic approach to dynamic systems, emphasizing theoretical principles and classic models in a wide variety of areas. Provides a particularly comprehensive theoretical development that includes chapters on positive dynamic systems and optimal control theory. Contains numerous problems.

✦ Table of Contents

Preface
......Page 5
Contents......Page 9
1. Dynamic Phenomena
......Page 15
2. Multivariable Systems
......Page 16
3. A Catalog of Examples
......Page 18
4. The Stages of Dynamic System Analysis......Page 24
1. Difference Equations
......Page 28
2. Existence and Uniqueness of Solutions
......Page 31
3. A First-Order Equation
......Page 33
4. Chain Letters and Amortization
......Page 35
5. The Cobweb Model
......Page 37
6. Linear Difference Equations
......Page 40
7. Linear Equations with Constant Coefficients
......Page 46
8. Differential Equations
......Page 52
9. Linear Differential Equations
......Page 54
10. Harmonic Motion and Beats
......Page 58
11. Problems
......Page 61
3 Linear Algebra
......Page 69
1. Fundamentals
......Page 70
2. Determinants
......Page 76
3. Inverses and the Fundamental Lemma
......Page 80
4. Vector Space
......Page 83
5. Transformations
......Page 87
6. Eigenvectors
......Page 91
7. Distinct Eigenvalues
......Page 94
8. Right and Left Eigenvectors
......Page 97
9. Multiple Eigenvalues
......Page 98
10. Problems
......Page 100
1. Systems of First-Order Equations
......Page 104
2. Conversion to State Form
......Page 109
3. Dynamic Diagrams
......Page 111
4. Homogeneous Discrete-Time Systems
......Page 113
5. General Solution to Linear Discrete-Time Systems
......Page 122
6. Homogeneous Continuous-Time Systems
......Page 127
7. General Solution to Linear Continuous-Time Systems
......Page 132
8. Embedded Statics
......Page 135
9. Problems
......Page 138
5 Linear Systems with Constant Coefficients
......Page 146
1. Geometric Sequences and Exponentials
......Page 147
2. System Eigenvectors
......Page 149
3. Diagonalization of a System
......Page 150
4. Dynamics of Right and Left Eigenvectors
......Page 156
5. Example: A Simple Migration Model
......Page 158
6. Multiple Eigenvalues
......Page 162
7. Equilibrium Points
......Page 164
8. Example: Survival Theory in Culture
......Page 166
9. Stability
......Page 168
10. Oscillations
......Page 174
11. Dominant Modes
......Page 179
12. The Cohort Population Model
......Page 184
13. The Surprising Solution to the Natchez Problem
......Page 188
14. Problems
......Page 193
1. Introduction
......Page 202
2. Positive Matrices
......Page 204
3. Positive Discrete-Time Systems
......Page 209
4. Quality in Herarchy---The Peter Principle......Page 213
5. Continuous-Time Positive Systems
......Page 218
6. Richardson's Theory of Arms Races
......Page 220
7. Comparative Statics for Positive Systems
......Page 225
8. Homans-Simon Model of Group Interaction
......Page 229
9. Problems
......Page 231
7 Markov Chains
......Page 238
1. Finite Markov Chains
......Page 239
2. Regular Markov Chains and Limiting Distributions
......Page 244
3. Classification of States
......Page 249
4. Transient State Analysis
......Page 253
5. Infinite Markov Chains
......Page 259
6. Problems
......Page 262
1. Inputs, Outputs, and Interconnections
......Page 268
2. z-Transforms
......Page 269
3. Transform Solution of Difference Equations
......Page 275
4. State Equations and Transforms
......Page 280
5. Laplace Transforms
......Page 286
6. Controllability
......Page 290
7. Observability
......Page 299
8. Canonical Forms
......Page 303
9. Feedback
......Page 310
10. Observers
......Page 314
11. Problems
......Page 323
1. Introduction
......Page 330
2. Equilibrium Points
......Page 334
3. Stability
......Page 336
4. Linearization and Stability
......Page 338
5. Example: The Principle of Competitive Exclusion
......Page 342
6. Liapunov Functions
......Page 346
7. Examples
......Page 353
8. Invariant Sets
......Page 359
9. A Linear Liapunov Function for Positive Systems
......Page 361
10. An Integral Liapunov Function
......Page 363
11. A Quadratic Liapunov Function for Linear Systems
......Page 364
12. Combined Liapunov Functions
......Page 367
13. General Summarizing Functions
......Page 368
14. Problems
......Page 370
10 Some Important Dynamic Systems......Page 378
1. Energy in Mechanics
......Page 379
2. Entropy in Thermodynamics
......Page 381
3. Interacting Populations
......Page 384
4. Epidemics
......Page 390
5. Stability of Competitive Economic Equilibria
......Page 392
6. Genetics
......Page 396
7. Problems
......Page 403
11 Optimal Control
......Page 407
1. The Basic Optimal Control Problem
......Page 408
2. Examples
......Page 415
3. Problems with Terminal Constraints
......Page 419
4. Free Terminal Time Problems
......Page 423
5. Linear Systems with Quadratic Cost
......Page 427
6. Discrete-Time Problems
......Page 430
7. Dynamic Programming
......Page 433
8. Stability and Optimal Control
......Page 439
9. Problems
......Page 441
References
......Page 450
Index
......Page 457