Linear dynamical systems, Volume 135 (Mathematics in Science and Engineering)

✍ Scribed by Casti (editor)

• Publisher: Academic Press
• Year: 1987
• Tongue: English
• Leaves: 371
• Category: Library

✦ Table of Contents

Front Cover
Linear Dynamical Systems
Copyright Page
Contents
Preface to the Revised Edition
Preface to the First Edition
Chapter 1. Basic Concepts, Problems, and Examples
1.1 Dynamical Systems, Inputs, and Outputs

1.3 Realizations
1.4 Controllability and Observability
1.5 Stability and Feedback
1.6 Optimality
1.7 Stochastic Disturbances
Notes and References
Chapter 2. Mathematical Description of Linear Dynamical Systems
2.1 Introduction
2.2 Dynamical Systems
2.3 External Description
2.4 Frequency-Domain Analysis
2.5 Transfer Functions
2.6 Impulse-Response Function
Notes and References
Chapter 3. Controllability and Reachability
3.1 Introduction
3.2 Basic Definitions
3.3 Time-Dependent Linear Systems
3.4 Discrete-Time Systems
3.5 Constant Systems
3.6 Positive Controllability
3.7 Relative Controllability
3.8 Conditional Controllability
3.9 Structural Controllability
3.10 Controllability and Transfer Functions
3.11 Systems with a Delay
Miscellaneous Exercises
Notes and References
Chapter 4. Observability/Constructibility
4.1 Introduction
4.2 Basic Definitions
4.3 Basic Theorems
4.4 Duality
4.5 Functional Analytic Approach to Observability
4.6 The Problem of Moments
Miscellaneous Exercises
Notes and References
Chapter 5. Structure Theorems and Canonical Forms
5.1 Introduction
5.2 State Variable Transformations
5.3 Control Canonical Forms
5.4 Observer Canonical Forms
5.5 Invariance of Transfer Functions
5.6 Canonical Forms and the Bezoutiant Matrix
5.7 The Feedback Group and Invariant Theory
Miscellaneous Exercises
Notes and References
Chapter 6. Realization Theory
6.1 Introduction
6.2 Algebraic Equivalence and Minimal Realizability
6.3 Construction of Realizations
6.4 Minimal Realization Algorithm
6.5 Examples
6.6 Realization of Transfer Functions
6.7 Uniqueness of Minimal Realizations
6.8 Partial Realizations
6.9 Reduced Order Models and Balanced Realizations
Miscellaneous Exercises
Notes and References
Chapter 7. Stability Theory
7.1 Introduction
7.2 Some Examples and Basic Concepts
7.3 Routh-Hurwicz Methods
7.4 Lyapunov Method
7.5 Frequency-Domain Techniques
7.6 Feedback Control Systems and Stability
7.7 Modal Control
7.8 Observers
7.9 Structural Stability
Miscellaneous Exercises
Notes and References
Chapter 8. The Linear-Quadratic-Gaussian Problem
8.1 Motivation and Examples
8.2 Open-Loop Solutions
8.3 The Maximum Principle
8.4 Some Computational Considerations
8.5 Feedback Solutions
8.6 Generalized X–Y Functions
8.7 Optimality versus Stability
8.8 A Low-Dimensional Alternative to the Algebraic Riccati Equation
8.9 Computational Approaches for Riccati Equations
8.10 Structural Stability of the Optimal Closed-Loop System
8.11 Inverse Problems
8.12 Linear Filtering Theory and Duality
8.13 The Separation Principle and Stochastic Control Theory
8.14 Discrete-Time Problems
8.15 Generalized X–Y Functions Revisited
Miscellaneous Exercises
Notes and References
Chapter 9. A Geometric-Algebraic View of Linear Systems
9.1 Algebra, Geometry, and Linear Systems
9.2 Mathematical Description of a Linear System

9.4 Some System-Theoretic Consequences
9.5 Transfer Functions
9.6 Realization of Transfer Functions
9.7 The Construction of Canonical Realizations
9.8 Partial Realizations
9.9 Pole-Shifting and Stability
9.10 Systems over Rings
9.11 Some Geometric Aspects of Linear Systems
9.12 Feedback, the McMillan Degree, and Kronecker Indices
9.13 Some Additional Ideas from Algebraic Geometry
9.14 Pole Placement for Linear Regulators
9.15 Multivariable Nyquist Criteria

Miscellaneous Exercises
Notes and References
Chapter 10. Infinite-Dimensional Systems
10.1 Finiteness as a System Property
10.2 Reachability and Controllability
10.3 Observability and Duality
10.4 Stability Theory
10.5 Realization Theory
10.6 The LQG Problem
10.7 Operator Riccati Equations and Generalized X–Y Functions
Miscellaneous Exercises
Notes and References
Index