Mathematical Control Theory by Eduardo D. Sontag
Mathematical Control Theory - Table of Contents
1. Introduction
2. Systems
3. Reachability and Controllability
4. Nonlinear Controllability
5. Feedback and Stabilization
6. Outputs
7. Observers and Dynamic Feedback
8. Optimality: Value Function
9. Optimality: Multipliers
10. Optimality: Minimum-Time for Linear Systems
What You Will Learn in Mathematical Control Theory
"Mathematical Control Theory: Deterministic Finite Dimensional Systems" by Eduardo D. Sontag is a foundational book that explains how mathematics is used to understand and control dynamic systems. It focuses on the theory behind systems that change over time, helping readers see how inputs can influence system behavior in a predictable way. The book is written for advanced students and researchers who want a deep, clear understanding of "control systems", not just practical recipes.
The text covers essential topics such as "controllability", "stability", and "feedback", with careful explanations and mathematical proofs. Both linear and nonlinear systems are explored, showing how abstract concepts apply to real-world models in engineering and science. Sontag places strong emphasis on "Lyapunov methods" and system behavior, making complex ideas easier to follow through logical structure and examples.
What makes this book stand out is its balance between rigor and insight. Rather than focusing on software or simulations, it builds strong theoretical foundations that support modern applications like robotics, automation, and networked systems. For readers interested in the mathematical backbone of "dynamical systems", this book remains a respected and influential resource in control theory.
Book Details & Specifications
Title:
Mathematical Control Theory by Eduardo D. Sontag
Publisher:
Springer
Year:
1998
Pages:
544
Type:
PDF
Language:
English
ISBN-10 #:
0387973664
ISBN-13 #:
978-0387973661
License:
External Educational Resource
Amazon:
Amazon
About the Author: Eduardo Daniel Sontag
The author Eduardo Daniel Sontag
is a renowned mathematician and professor best known for his contributions to "control theory" and "dynamical systems". His work focuses on understanding how complex systems evolve and how mathematical tools can be used to influence system behavior in a reliable way. He has made major advances in "nonlinear systems", "stability analysis", and "controllability", with research that impacts engineering, biology, and system modeling. As an author, Sontag is valued for clear explanations that connect deep theory with practical insight, strengthening the foundations of modern "system control".
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