Introduction to Dynamic Systems Theory,

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.

DAVID G. LUENBERGER is a professor in the School of Engineering at Stanford University. He has published four textbooks and over 70 technical papers. Professor Luenberger is a Fellow of the Institute of Electrical and Electronics Engineers and recipient of the 1990 Bode Lecture Award. His current research is mainly in investment science, economics, and planning.

Introduction

Dynamic Phenomena

1

(1)

Multivariable Systems

2

(2)

A Catalog of Examples

4

(6)

The Stages of Dynamic System Analysis

10

(4)

Difference And Differential Equations

Difference Equations

14

(3)

Existence and Uniqueness of Solutions

17

(2)

A First-Order Equation

19

(2)

Chain Letters and Amortization

21

(2)

The Cobweb Model

23

(3)

Linear Difference Equations

26

(6)

Linear Equations with Constant Coefficients

32

(6)

Differential Equations

38

(2)

Linear Differential Equations

40

(4)

Harmonic Motion and Beats

44

(3)

Problems

47

(9)

Notes and References

54

(2)

Linear Algebra

Algebraic Properties

Fundamentals

56

(6)

Determinants

62

(4)

Inverses and the Fundamental Lemma

66

(3)

Geometric Properties

Vector Space

69

(4)

Transformations

73

(4)

Eigenvectors

77

(3)

Distinct Eigenvalues

80

(3)

Right and Left Eigenvectors

83

(1)

Multiple Eigenvalues

84

(2)

Problems

86

(4)

Notes and References

89

(1)

Linear State Equations

Systems of First-Order Equations

90

(5)

Conversion to State Form

95

(2)

Dynamic Diagrams

97

(2)

Homogeneous Discrete-Time Systems

99

(9)

General Solution to Linear Discrete-Time Systems

108

(5)

Homogeneous Continuous-Time Systems

113

(5)

General Solution to Linear Continuous-Time Systems

118

(3)

Embedded Statics

121

(3)

Problems

124

(9)

Notes and References

130

(3)

Linear Systems With Constant Coefficients

Geometric Sequences and Exponentials

133

(2)

System Eigenvectors

135

(1)

Diagonalization of a System

136

(6)

Dynamics of Right and Left Eigenvectors

142

(2)

Example: A Simple Migration Model

144

(4)

Multiple Eigenvalues

148

(2)

Equilibrium Points

150

(2)

Example: Survival Theory in Culture

152

(2)

Stability

154

(6)

Oscillations

160

(5)

Dominant Modes

165

(5)

The Cohort Population Model

170

(4)

The Surprising Solution to the Natchez Problem

174

(5)

Problems

179

(9)

Notes and References

186

(2)

Positive Linear Systems

Introduction

188

(2)

Positive Matrices

190

(5)

Positive Discrete-Time Systems

195

(4)

Quality in a Hierarchy---The Peter Principle

199

(5)

Continuous-Time Positive Systems

204

(2)

Richardson's Theory of Arms Races

206

(5)

Comparative Statics for Positive Systems

211

(4)

Homans-Simon Model of Group Interaction

215

(2)

Problems

217

(8)

Notes and References

222

(3)

Markov Chains

Finite Markov Chains

225

(5)

Regular Markov Chains and Limiting Distributions

230

(5)

Classification of States

235

(4)

Transient State Analysis

239

(6)

Infinite Markov Chains

245

(3)

Problems

248

(6)

Notes and References

253

(1)

Concepts of Control

Inputs, Outputs, and Interconnections

254

(1)

Transform Methods

z-Transforms

255

(6)

Transform Solution of Difference Equations

261

(5)

State Equations and Transforms

266

(6)

Laplace Transforms

272

(4)

State Space Methods

Controllability

276

(9)

Observability

285

(4)

Canonical Forms

289

(7)

Feedback

296

(4)

Observers

300

(9)

Problems

309

(7)

Notes and References

314

(2)

Analysis of Nonlinear Systems

Introduction

316

(4)

Equilibrium Points

320

(2)

Stability

322

(2)

Linearization and Stability

324

(4)

Example: The Principle of Competitive Exclusion

328

(4)

Liapunov Functions

332

(7)

Examples

339

(6)

Invariant Sets

345

(2)

A Linear Liapunov Function for Positive Systems

347

(2)

An Integral Liapunov Function

349

(1)

A Quadratic Liapunov Function for Linear Systems

350

(3)

Combined Liapunov Functions

353

(1)

General Summarizing Functions

354

(2)

Problems

356

(9)

Notes and References

363

(2)

Some Important Dynamic Systems

Energy in Mechanics

365

(2)

Entropy in Thermodynamics

367

(3)

Interacting Populations

370

(6)

Epidemics

376

(2)

Stability of Competitive Economic Equilibria

378

(4)

Genetics

382

(7)

Problems

389

(5)

Notes and References

391

(3)

Optimal Control

The Basic Optimal Control Problem

394

(7)

Examples

401

(4)

Problems with Terminal Constraints

405

(4)

Free Terminal Time Problems

409

(4)

Linear Systems with Quadratic Cost

413

(3)

Discrete-Time Problems

416

(3)

Dynamic Programming

419

(6)

Stability and Optimal Control

425

(2)

Problems

427

(9)

Notes and References

435

(1)

References

436

(5)

Index

441

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Introduction to Dynamic Systems Theory, Models, and Applications

Summary

Author Biography

Table of Contents

Supplemental Materials