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Linear System Theory and Design

Fourth Edition

Chi-Tsong Chen

Publication Date - November 2012

ISBN: 9780199959570

400 pages
7-1/2 x 9-1/4 inches

In Stock

Retail Price to Students: $159.95

A succinct and rigorous introduction to linear and multivariable system 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 www.oup.com/us/chen 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

New to this Edition

  • All examples using MATLAB have been updated using the R2011a version
  • Chapter 1 provides a brief history and overview of the subject
  • Chapter 2 has been restructured in order to discuss four types of equations and to give reasons for focusing on rational transfer functions and state-space equations
  • Chapter 4 includes a new section on SISO realizations and expanded discussions of computer computation and real-time processing of state-space equations
  • Chapter 7 includes a new section on complete characterization

About the Author(s)

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

Previous Publication Date(s)

September 1998
June 1995


"This book offers a superior and accessible presentation of theory."--Oscar González, Old Dominion University

"Chen has an excellent writing style. His book is concise, brief, and to the point. It is very informative and engaging. Simply perfect for an engineering textbook."--Amr M. Baz, University of Maryland, College Park

"Linear System Theory and Design provides the definitive version of how to present this material."--Douglas K. Lindner, Virginia Polytechnic Institute and State University

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

Teaching Resources

  • Companion website at www.oup.com/us/chen 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

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