Mathematical Control Theory by Eduardo D. Sontag
Mathematical Control Theory - Table of Contents
- 1. Introduction
- 2. Systems and input output state space systems realization
- 3. Reachability and Controllability and linear reachability matrix controllability criteria
- 4. Nonlinear Controllability and nonlinear controllability lie algebra rank condition
- 5. Feedback and Stabilization and feedback stabilization control lyapunov functions
- 6. Outputs and observability state estimation detectability
- 7. Observers and Dynamic Feedback and dynamic observers separation principle state feedback
- 8. Optimality: Value Function and optimal control dynamic programming value function hjb
- 9. Optimality: Multipliers and pontryagin maximum principle Lagrange multipliers
- 10. Optimality: Minimum-Time for Linear Systems and minimum time control linear systems bang bang principle
What You Will Learn in Mathematical Control Theory
Targeted at graduate students and mathematical researchers, Mathematical Control Theory: Deterministic Finite Dimensional Systems by Eduardo D. Sontag provides an in-depth analytical treatment of modern deterministic control systems. Across 10 systematically organized chapters, this work examines linear and non-linear system state spaces, reachability criteria, non-linear accessibility via Lie brackets, feedback stabilization, dynamic observers, dynamic programming value functions, Pontryagin's maximum principle, and time-optimal linear control.
Author Eduardo D. Sontag bridges topological, algebraic, and differential-geometric perspectives to create a unified framework for dynamical systems. Readers are guided through pole placement strategies, Control Lyapunov Functions, Kalman filter observers, Hamilton-Jacobi-Bellman equations, and multiplier methods with complete mathematical rigor.
Prized for its theoretical depth, broad conceptual scope, and precise exposition, this volume stands as one of the best mathematical control theory textbooks pdf available for study. It equips control engineers and theoretical mathematicians with core analytical tools for mastering deterministic control theory with confidence.
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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