Thomas Kailath's 1980 textbook, Linear Systems , is a foundational, mathematically rigorous text bridging classical transfer-function methods with modern state-space techniques. It covers essential control theory concepts such as controllability, observability, and realization theory, maintaining relevance in graduate-level engineering education. For a digital version of the text, see ResearchGate
(PDF) Review of 'Linear Systems' (T. Kailath, 1980) - ResearchGate
Linear Systems by Thomas Kailath: A Comprehensive Review
Introduction
"Linear Systems" by Thomas Kailath is a renowned textbook that has been a staple in the field of electrical engineering, control systems, and signal processing for decades. First published in 1980, the book has undergone several reprints and revisions, solidifying its position as a classic in the field. In this blog post, we will review the book's content, highlighting its key features, strengths, and weaknesses.
About the Author
Thomas Kailath is a prominent figure in the field of electrical engineering, with a distinguished career spanning over six decades. He is a Professor Emeritus of Electrical Engineering at Stanford University, where he held the Hitachi America Professorship. Kailath is a Fellow of the Institute of Electrical and Electronics Engineers (IEEE) and a member of the National Academy of Engineering.
Book Overview
"Linear Systems" is a comprehensive textbook that covers the fundamental concepts of linear systems, including:
Key Features
Some notable features of "Linear Systems" include:
Strengths
The strengths of "Linear Systems" include: thomas kailath linear systems pdf
Weaknesses
Some potential weaknesses of the book include:
Conclusion
"Linear Systems" by Thomas Kailath is a comprehensive and mathematically rigorous textbook that has been a staple in the field of electrical engineering, control systems, and signal processing for decades. While it may have some limitations, the book remains an excellent resource for students and researchers seeking a deep understanding of linear systems. If you're interested in learning about linear systems, we highly recommend "Linear Systems" by Thomas Kailath.
Download PDF
If you're interested in downloading a PDF version of "Linear Systems" by Thomas Kailath, we recommend searching for online repositories or digital libraries that provide access to the book. Some popular options include:
Please note that downloading a PDF version of the book may be subject to copyright restrictions. We encourage readers to purchase a physical copy or access the book through legitimate channels.
References
Thomas Kailath’s Linear Systems (1980) is widely considered the "bible" of state-space methods. If you are hunting for a PDF version via a blog post, you are likely looking for a deep dive into why this 40-year-old textbook remains the gold standard for control theory and signal processing. Why Every Control Engineer’s Blog Mentions Kailath
While modern textbooks might be easier to carry, Kailath’s work is unmatched in its mathematical rigor and breadth. Most blog discussions center on these core strengths:
The Unifying Perspective: Kailath doesn't just teach linear algebra; he bridges the gap between transfer functions (the frequency domain) and state-space models (the time domain).
Mathematical Depth: It covers topics many modern books skim over, such as polynomial matrix descriptions and the Kronecker product, which are essential for advanced research. Thomas Kailath's 1980 textbook, Linear Systems , is
Historical Context: The book provides "Notes and References" at the end of each chapter that read like a history of 20th-century engineering, tracing the lineage of ideas from Kalman, Wiener, and others. Accessing the Text
Finding a legitimate PDF can be tricky due to copyright, but here are the common ways students and researchers access it:
Prentice-Hall & Reprints: Originally published by Prentice-Hall, the book is often available through university libraries.
Open Library & Internet Archive: Some educational repositories host borrowable digital copies for students.
Used Market: Because it’s a "legacy" book, many engineers recommend picking up a physical copy; its density makes it a better reference shelf staple than a quick digital skim. Key Takeaways for Your Studies
If you're reading this for a course or self-study, focus on Chapter 2 (State-Space Representations) and Chapter 6 (Stability). These sections contain the foundational proofs for controllability and observability that define the field.
This section integrates "classical" control concepts with state-space theory.
Week 1: State-space fundamentals, matrix exponentials, solutions of linear systems.
Week 2: Controllability/observability, canonical forms, minimal realizations.
Week 3: State feedback, observers, LQR and Riccati equations.
Week 4: Kalman filtering, stochastic estimation, numerical issues and case studies.
(Work through proofs and 1–2 example problems per topic.)
Kailath, T. (1980). Linear Systems (Vol. 156). Englewood Cliffs, NJ: Prentice-Hall.
The book provides a rigorous treatment of systems described by polynomial matrices ($P(s) = D(s)^-1N(s)$), offering a middle ground between the high-level abstraction of state space and the scalar nature of transfer functions.
Style:
Audance:
If you are a graduate student or researcher in control, signal processing, or theoretical electrical engineering, Thomas Kailath’s Linear Systems is a canonical work that rewards deep study. While obtaining a free PDF copy is technically copyright infringement, the knowledge contained within—especially the geometric approach to controllability/observability and the mastery of polynomial matrix descriptions—is considered essential for a professional understanding of the field. For legal access, check university library portals, interlibrary loan, or used book marketplaces.
Thomas Kailath 's Linear Systems (1980) is widely considered a foundational textbook in control theory and engineering. While the full copyrighted text is available for viewing on platforms like Scribd and PDFCOFFEE, the book's core features distinguish it from standard texts by focusing on the interplay between systems and mathematical concepts. Key Features of " Linear Systems
System-First Approach: Kailath prioritizes "systems concepts" over pure mathematics, moving away from starting with abstract vector spaces to instead integrate math as it serves system needs.
Matrix Fraction Descriptions (MFD): The text provides a pioneering, comprehensive treatment of MFDs and the theory of polynomial and rational matrices.
State-Space Mastery: It offers deep dives into state feedback compensator design, observer theory, and realization concepts like controllability and observability.
Focus on Scalar Systems: Nearly half the book (Chapters 1–4) is dedicated to constant scalar systems, providing a solid foundation before moving into more complex multivariable realization.
Historical Context: Unlike many modern technical books, it often includes historical perspectives to show how control theory grew out of specific technical needs. Chapter Overview
Introduction: Basic math review and Laplace transform subtleties.
State-Space Descriptions: Realization, controllability, and observability in constant scalar systems.
Linear State-Variable Feedback: Practical application of controllability.
Asymptotic Observers: Compensator design based on observability.
Algebraic Complements: Advanced vector spaces, geometric ideas, and Nerode equivalence. Vector spaces and linear algebra : The book
Multivariable Realization Theory: Extending scalar concepts to multivariable systems.
For academic reviews and deeper technical summaries, you can refer to the IEEE Xplore Book Review or the SIAM Review. Linear Systems By Thomas Kailath - sciphilconf.berkeley.edu