## Electrical and Computer Engineering Faculty Scholarship

#### Title

Fundamentals of Linear State Space Systems

Book

1999

#### Keywords

linear systems, matrices, linear algebra, control theory

#### Abstract

This book addresses two primary deficiencies in the linear systems textbook market: a lack of development of state space methods from the basic principles and a lack of pedagogical focus. The book uses the geometric intuition provided by vector space analysis to develop in a very sequential manner all the essential topics in linear state system theory that a senior or beginning graduate student should know. It does this in an ordered, readable manner, with examples drawn from several areas of engineering. Because it derives state space methods from linear algebra and vector spaces and ties all the topics together with diverse applications, this book is suitable for students from any engineering discipline, not just those with control systems backgrounds and interests. It begins with the mathematical preliminaries of vectors and spaces, then emphasizes the geometric properties of linear operators. It is from this foundation that the studies of stability, controllability and observability, realizations, state feedback, observers, and Kalman filters are derived. There is a direct and simple path from one topic to the next. The book includes both discrete- and continuous-time systems, introducing them in parallel and emphasizing each in appropriate context. Time-varying systems are discussed from generality and completeness, but the emphasis is on time-invariant systems, and only in time-domain; there is no treatment of matrix fraction descriptions or polynomial matrices. Tips for using MATLAB are included in the form of margin notes, which are placed wherever topics with applicable MATLAB commands are introduced. These notes direct the reader to an appendix, where a MATLAB command reference explains command usage. However, an instructor or student who is not interested in MATLAB usage can easily skip these references without interrupting the flow of text.

Note that the main file is the Preface to the book. The other files are:

PART I: MATHEMATICAL INTRODUCTION TO STATE SPACE

Chapter 1: Models of Linear Systems

Chapter 2: Vectors and Vecor Spaces

Chapter 3: Linear Operators on Vector Spaces

Chapter 4: Eigenvalues and Eigenvectors

Chapter 5: Functions of Vectors and Matrices

PART II: ANALYSIS AND CONTROL OF STATE SPACE SYSTEMS

Chapter 6: Solutions to State Space Equations

Chapter 7: System Stability

Chapter 8: Controllability and Observability

Chapter 9: System Realizations

Chapter 10: State Feedback and Observers

Chapter 11: Introduction to Optimal Control and Estimation

APPENDIX A: MATHEMATICAL TABLES AND IDENTITIES

APPENDIX B: MATLAB COMMAND SUMMARIES

INDEX

Please NOTE: The main document is just the Preface of the book, and that the additional documents are the individual chapters

This text was previously published and distributed by McGraw-Hill Higher Education. I recently gained the rights to distribute it, and am doing so free of charge.

Thank you to all my previous adopters.

toc_updated.pdf (158 kB)

chapter1_updated.pdf (813 kB)
Models of Linear Systems

chapter2_updated.pdf (951 kB)
Vectors and Vector Spaces

chapter3_updated.pdf (1126 kB)
Linear Operators on Vector Spaces

chapter4_updated.pdf (740 kB)
Eigenvalues and Eigenvectors

chapter5_updated.pdf (674 kB)
Functions of Vectors and Matrices

chapter6_updated.pdf (654 kB)
Solutions to State Equations

chapter7_updated.pdf (795 kB)
System Stability

chapter8_updated.pdf (849 kB)
Controllability and Observability

chapter9_updated.pdf (557 kB)
System Realizations

chapter10_updated.pdf (911 kB)
State Feedback and Observers

chapter11_updated.pdf (1354 kB)
Introduction to Optimal Control and Estimation

Index_updated.pdf (238 kB)
appendxa_updated.pdf (250 kB)
Mathematics tables and identities

appendxb_updated.pdf (487 kB)
MATLAB Commands

COinS