Linear System Theory / by Frank M. Callier, Charles A. Desoer.

Format:

Book

Author/Creator:

Callier, Frank M., author.

Desoer, Charles A., author.

Contributor:

SpringerLink (Online service)

Series:

Springer texts in electrical engineering 1431-8482

Springer Texts in Electrical Engineering, 1431-8482

Language:

English

Subjects (All):

Electrical engineering.

Applied mathematics.

Engineering mathematics.

System theory.

Calculus of variations.

Communications Engineering, Networks.

Electrical Engineering.

Mathematical and Computational Engineering.

Systems Theory, Control.

Calculus of Variations and Optimal Control; Optimization.

Local Subjects:

Communications Engineering, Networks.

Electrical Engineering.

Mathematical and Computational Engineering.

Systems Theory, Control.

Calculus of Variations and Optimal Control; Optimization.

Physical Description:

1 online resource.

Edition:

First edition 1991.

Contained In:

Springer Nature eBook

Place of Publication:

New York, NY : Springer New York : Imprint: Springer, 1991.

System Details:

text file PDF

Summary:

This book is the result of our teaching over the years an undergraduate course on Linear Optimal Systems to applied mathematicians and a first-year graduate course on Linear Systems to engineers. The contents of the book bear the strong influence of the great advances in the field and of its enormous literature. However, we made no attempt to have a complete coverage. Our motivation was to write a book on linear systems that covers finite- dimensional linear systems, always keeping in mind the main purpose of engineering and applied science, which is to analyze, design, and improve the performance of phy- sical systems. Hence we discuss the effect of small nonlinearities, and of perturbations of feedback. It is our on the data; we face robustness issues and discuss the properties hope that the book will be a useful reference for a first-year graduate student. We assume that a typical reader with an engineering background will have gone through the conventional undergraduate single-input single-output linear systems course; an elementary course in control is not indispensable but may be useful for motivation. For readers from a mathematical curriculum we require only familiarity with techniques of linear algebra and of ordinary differential equations.

Contents:

1 Introduction

1.1 Science and Engineering

1.2 Physical Systems, Models, and Representations

1.3 Robustness

2 The System RepresentationR(·) = [A(·),B(·),C(·),D(·)]

2.1 Fundamental Properties ofR(·)

2.2 Applications

2d The Discrete-Time System RepresentationRd(·) = [A(·),B(·),C(·),D(·)]

2d.1 Fundamental Properties ofRd(·)

2d.2 Application: Periodically Varying Recursion Equations

3 The System RepresentationR= [A,B,C,D], Part I

3.1 Preliminaries

3.2 General Properties ofR= [A,B,C,D]

3.3 Properties of R when A has a Basis of Eigenvectors

3d The Discrete-Time System Representation Rd = [A,B,C,D]

3d.1 Preliminaries

3d.2 General Properties of Rd

3d.3 Properties of Rd when A has a Basis of Eigenvectors

4 The System Representation R = [A,B,C,D], Part II

4.1 Preliminaries

4.2 Minimal Polynomial

4.3 Decomposition Theorem

4.4 The Decomposition of a Linear Map

4.5 Jordan Form

4.6 Function of a Matrix

4.7 Spectral Mapping Theorem

4.8 The Linear Map X ? AX+XB

5 General System Concepts

5.1 Dynamical Systems

5.2 Time-Invariant Dynamical Systems

5.3 Linear Dynamical Systems

5.4 Equivalence

6 Sampled Data Systems

6.1 Relation BetweenL- and z-Transforms

6.2 D/A Converter

6.3 A/D Converter

6.4 Sampled-Data System

6.5 Example

7 Stability

7.1 I/O Stability

7.2 State Related Stability Concepts and Applications

7d Stability: The Discrete-Time Case

7d.1 I/O Stability

7d.2 State Related Stability Concepts

8 Controllability and Observability

8.1 Controllability and Observability of Dynamical Systems

8.2 Controllability of the Pair (A(·),B(·))

8.3 Observability of the Pair (C(·),A(·))

8.4 Duality

8.5 Linear Time-Invariant Systems

8.6 Kalman Decomposition Theorem

8.7 Hidden Modes, Stabilizability, and Detectability

8.8 Balanced Representations

8.9 Robustness of Controllability

8d Controllability and Observability: The Discrete-Time Case

8d.1 Controllability and Observability of Dynamical Systems

8d.2 Reachability and Controllability of the Pair (A(·),B(·))

8d.3 Observability of the Pair (C(·),A(·))

8d.4 Duality

8d.5 Linear Time-Invariant Systems

8d.6 Kalman Decomposition Theorem

8d.7 Stabilizability and Detectability

9 Realization Theory

9.1 Minimal Realizations

9.2 Controllable Canonical Form

10 Linear State Feedback and Estimation

10.1 Linear State Feedback

10.2 Linear Output Injection and State Estimation

10.3 State Feedback of the Estimated State

10.4 Infinite Horizon Linear Quadratic Optimization

10d.4 Infinite Horizon Linear Quadratic Optimization. The Discrete-Time Case

11 Unity Feedback Systems

11.1 The Feedback System ?c

11.2 Nyquist Criterion

11.3 Robustness

11.4 Kharitonov's Theorem

11.5 Robust Stability Under Structured Perturbations

11.6 Stability Under Arbitrary Additive Plant Perturbations

11.7 Transmission Zeros

Appendix A Linear Maps and Matrix Analysis

A.1 Preliminary Notions

A.2 Rings and Fields

A.3 Linear Spaces

A4. Linear Maps

AS. Matrix Representation

A.5.1 The Concept of Matrix Representation

A.5.2 Matrix Representation and Change of Basis

A.5.3 Range and Null Space: Rank and Nullity

A.5.4 Echelon Forms of a Matrix

A.6 Notmed Linear Spaces

A.6.1 Norms

A.6.2 Convergence

A.6.3 Equivalent Norms

A.6.4 The Lebesgue Spaces 1P and LP [Tay.1]

A.6.5 Continuous Linear Transformations

A.7 The Adjoint of a Linear Map

A.7.1 Inner Products

A.7.2 Adjoints of Continuous Linear Maps

A.7.3 Properties of the Adjoint

A.7.4 The Finite Rank Operator Fundamental Lemma

A.7.5 Singular Value Decomposition (SVD)

Appendix B Differential Equations

BA Existence and Uniqueness of Solutions

B.1.1 Assumptions

B.1.2 Fundamental Theorem

B.1.3 Construction of a Solution by Iteration

B.1.4 The Bellman-Gronwall Inequality

B.1.5 Uniqueness

B.2 Initial Conditions and Parameter Perturbations

B.3 Geometric Interpretation and Numerical Calculations

Appendix C Laplace Transforms

C.1 Definition of the Laplace Transform

C.2 Properties of Laplace Transforms

Appendix D the z-Transform

D.1 Definition of the z-Transform

D.2 Properties of the z-Transform

References

Abbreviations

Mathematical Symbols.

Other Format:

Printed edition:

ISBN:

9781461209577

Access Restriction:

Restricted for use by site license.