George J. Pappas
Cover of Linear Systems Theory: From Linear Algebra to the Kalman Filter

Pella Press · Forthcoming January 1, 2027

Linear Systems Theory

From Linear Algebra to the Kalman Filter

State-space theory in the time domain, for graduate students and researchers in control, robotics, signal processing, and machine learning. Linear algebra is the only prerequisite.

Free e-book (PDF) Free Course Slides (PDF) Paperback on Amazon

All available January 1, 2027

About the Book

  • Twenty-six chapters, from linear algebra to LQG control
  • Stability, controllability, observability and realization
  • Feedback design, LQR and the Kalman filter
  • More than 300 worked examples and 400 exercises
  • Built on ESE 5000 at Penn, taught since 2001

Contents

Part I · Linear Algebra 1Introduction to Vector Spaces 2Introduction to Linear Maps 3Least Squares Theory 4Matrix Decompositions
Part II · Linear Systems 5Linear System Models 6Linear Systems and Functions of a Matrix 7The Response of Continuous-Time Linear Systems 8The Response of Time-Varying Linear Systems
Part III · Stability 9Lyapunov Stability 10Stability of Linear Time-Invariant Systems 11Stability of Time-Varying Linear Systems 12Input–Output Stability
Part IV · Controllability and Observability 13Controllability 14Observability 15The Kalman Decomposition 16Realization and Model Reduction
Part V · Feedback Design 17Eigenvalue Placement by State Feedback 18State Observers and Output Feedback 19Output Regulation
Part VI · Optimal Control 20The Finite-Horizon Linear Quadratic Regulator 21Infinite-Horizon LQR and the Algebraic Riccati Equation 22Continuous-Time LQR
Part VII · Stochastic Control and Estimation 23Linear Quadratic Stochastic Control 24Optimal Linear Estimation 25The Kalman Filter 26Linear Quadratic Gaussian Control

Afterword: Beyond Linear Systems · Notes and References · Index

For Instructors

Course slides for every chapter will be posted here as free PDFs on January 1, 2027. Instructors at accredited institutions also receive the instructor’s edition of the book, with solutions to all exercises, and the LaTeX source of the slides. Email pellapressbooks@gmail.com and say which course you plan to use the book for.

How to Cite

George J. Pappas, Linear Systems Theory: From Linear Algebra to the Kalman Filter. Pella Press, 2027. ISBN 979-8-9984760-0-6.

BibTeX

@book{pappas2027linear,
  author    = {George J. Pappas},
  title     = {Linear Systems Theory: From Linear Algebra to the Kalman Filter},
  publisher = {Pella Press},
  year      = {2027},
  isbn      = {979-8-9984760-0-6}
}

Details

Publisher · Pella Press Available · January 1, 2027 ISBN · 979-8-9984760-0-6 Format · 703 pages, 7.44 × 9.69 in Paperback · $39.99 on Amazon Free e-book (PDF) · posted on this page January 1, 2027 Free course slides (PDF) · posted on this page January 1, 2027

Course

ESE 5000 Linear Systems Theory, University of Pennsylvania Teaching page →