Pub. Date:
Oxford University Press
Linear System Theory and Design

Linear System Theory and Design

by Chi-Tsong Chen, Chi-Tsong Chen


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Linear System Theory and Design

Striking a balance between theory and applications, Linear System Theory and Design, Fourth Edition, uses simple and efficient methods to develop results and design procedures that students can readily employ.

Ideal for advanced undergraduate courses and first-year graduate courses in linear systems and multivariable system design, it is also a helpful resource for practicing engineers.


Companion website at contains PowerPoint-based versions of the figures from the text (available to adopters of the text)

An Instructor's Solutions Manual is available to adopters

Product Details

ISBN-13: 9780195392074
Publisher: Oxford University Press
Publication date: 02/28/2009
Pages: 352
Product dimensions: 9.25(w) x 7.52(h) x 0.73(d)

About the Author

Chi-Tsong Chen is Professor Emeritus of Electrical and Computer Engineering at Stony Brook University, New York.

Table of Contents

1. Introduction
1.1. Introduction
1.2. Overview
2. Mathematical Descriptions of Systems
2.1. Introduction
2.2. Causality, Lumpedness, and Time-Invariance
2.3. Linear Time-Invariant (LTI) Systems
2.4. Linear Time-Varying Systems
2.5. RLC circuits—Comparisons of Various Descriptions
2.6. Mechanical and Hydraulic Systems
2.7. Proper Rational Transfer Functions
2.8. Discrete-Time Linear Time-Invariant Systems
2.9. Concluding Remarks
3. Linear Algebra
3.1. Introduction
3.2. Basis, Representation, and Orthonormalization
3.3. Linear Algebraic Equations
3.4. Similarity Transformation
3.5. Diagonal Form and Jordan Form
3.6. Functions of a Square Matrix
3.7. Lyapunov Equation
3.8. Some Useful Formula
3.9. Quadratic Form and Positive Definiteness
3.10. Singular Value Decomposition
3.11. Norms of Matrices
4. State-Space Solutions and Realizations
4.1. Introduction
4.2. General Solution of CT LTI State-Space Equations
4.3. Computer Computation of CT State-Space Equations
4.4. Equivalent State Equations
4.5. Realizations
4.6. Solution of Linear Time-Varying (LTV) Equations
4.7. Equivalent Time-Varying Equations
4.8. Time-Varying Realizations
5. Stability
5.1. Introduction
5.2. Input-Output Stability of LTI Systems
5.3. Discrete-Time Case
5.4. Internal Stability
5.5. Lyapunov Theorem
5.6. Stability of LTV Systems
6. Controllability and Observability
6.1. Introduction
6.2. Controllability
6.3. Observability
6.4. Canonical Decomposition
6.5. Conditions in Jordan-Form Equations
6.6. Discrete-Time State-Space Equations
6.7. Controllability After Sampling
6.8. LTV State-Space Equations
7. Minimal Realizations and Coprime Fractions
7.1. Introduction
7.2. Implications of Coprimeness
7.3. Computing Coprime Fractions
7.4. Balanced Realization
7.5. Realizations from Markov Parameters
7.6. Degree of Transfer Matrices
7.7. Minimal Realizations- Matrix Case
7.8. Matrix Polynomial Fractions
7.9. Realization from Matrix Coprime Fractions
7.10. Realizations from Matrix Markov Parameters
7.11. Concluding Remarks
8. State Feedback and State Estimators
8.1. Introduction
8.2. State Feedback
8.3. Regulation and Tracking
8.4. State Estimator
8.5. Feedback from Estimated States
8.6. State feedback—MIMO case
8.7. State Estimators—MIMO case
8.8. Feedback from Estimated States—MIMO Case
9. Pole Placement and Model Matching
9.1. Introduction
9.2. Preliminary—Matching Coefficients
9.3. Unity-Feedback Configuration-Pole Placement
9.4. Implementable Transfer Functions
9.5. MIMO Unity Feedback Systems
9.6. MIMO Model Matching—Two-Parameter Configuration
9.7. Concluding Remarks
Answers to Selected Problems

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