(Please note: book is copyrighted by Springer-Verlag. Springer has kindly allowed me to place a copy on the web, as a reference and for ease of web searches. Please consider buying your own hardcopy.)

Precise reference:

Eduardo D. Sontag, *Mathematical Control Theory:
Deterministic Finite Dimensional Systems.
Second Edition*, Springer,
New York, 1998.
(531+xvi pages, ISBN 0-387-984895)

Series: Textbooks in Applied Mathematics, Number 6. Hardcover, approx $55.00

Order in USA from 1-800-SPRINGER or from amazon.com.

First Edition's
**web
** page.

(Errata, revisions, and some comments, all regarding the first edition,
are included there. No errata posted since mid 1997.)

Publicity Blurb:

This textbook introduces the core concepts and results of Control and System Theory. Unique in its emphasis on foundational aspects, it takes a "hybrid" approach in which basic results are derived for discrete and continuous time scales, and discrete and continuous state variables. Primarily geared towards mathematically advanced undergraduate or graduate students, it may also be suitable for a second engineering course in control which goes beyond the classical frequency domain and state-space material. The choice of topics, together with detailed end-of-chapter links to the bibliography, makes it an excellent research reference as well.

The Second Edition constitutes a substantial revision and extension of the First Edition, mainly adding or expanding upon advanced material, including: Lie-algebraic accessibility theory, feedback linearization, controllability of neural networks, reachability under input constraints, topics in nonlinear feedback design (such as backstepping, damping, control-Lyapunov functions, and topological obstructions to stabilization), and introductions to the calculus of variations, the maximum principle, numerical optimal control, and linear time-optimal control.

Also covered, as in the First Edition, are notions of systems and automata theory, and the algebraic theory of linear systems, including controllability, observability, feedback equivalence, and minimality; stability via Lyapunov, as well as input/output methods; linear-quadratic optimal control; observers and dynamic feedback; Kalman filtering via deterministic optimal observation; parametrization of stabilizing controllers, and facts about frequency domain such as the Nyquist criterion.

From the reviews of the first edition:

Mathematical Reviews

Zentralblatt fur Mathematik

IEEE Transactions on Automatic Control

Chapter and Section Headings:

Introduction

What Is Mathematical
Control Theory?

Proportional-Derivative
Control

Digital Control

Feedback Versus
Precomputed Control

State-Space
and Spectrum Assignment

Outputs and
Dynamic Feedback

Dealing with
Nonlinearity

A Brief Historical
Background

Some Topics
Not Covered Systems

Basic
Definitions

I/O Behaviors

Discrete-Time

Linear Discrete-Time
Systems

Smooth Discrete-Time
Systems

Continuous-Time

Linear Continuous-Time
Systems

Linearizations
Compute Differentials

More on Differentiability

Sampling

Volterra Expansions

Notes and Comments

Reachability
and Controllability

Basic Reachability
Notions

Time-Invariant
Systems

Controllable
Pairs of Matrices

Controllability
Under Sampling

More on Linear
Controllability

Bounded Controls

First-Order
Local Controllability

Controllability
of Recurrent Nets

Piecewise Constant
Controls

Notes and Comments

Nonlinear
Controllability

Lie Brackets

Lie Algebras
and Flows

Accessibility
Rank Condition

Ad, Distributions,
and Frobenius' Theorem

Necessity of
Accessibility Rank Condition

Additional
Problems

Notes and Comments

Feedback
and Stabilization

Constant Linear
Feedback

Feedback Equivalence

Feedback Linearization

Disturbance
Rejection and Invariance

Stability and
Other Asymptotic Notions

Unstable and
Stable Modes

Lyapunov and
Control-Lyapunov Functions

Linearization
Principle for Stability

Introduction
to Nonlinear Stabilization

Notes and Comments

Outputs

Basic Observability
Notions

Time-Invariant
Systems

Continuous-Time
Linear Systems

Linearization
Principle for Observability

Realization
Theory for Linear Systems

Recursion and
Partial Realization

Rationality
and Realizability

Abstract Realization
Theory

Notes and Comments

Observers
and Dynamic Feedback

Observers and
Detectability

Dynamic Feedback

External Stability
for Linear Systems

Frequency-Domain
Considerations

Parametrization
of Stabilizers

Notes and Comments

Optimality:
Value Function

Dynamic Programming

Linear Systems
with Quadratic Cost

Tracking and
Kalman Filtering

Infinite-Time
(Steady-State) Problem

Nonlinear Stabilizing
Optimal Controls

Notes and Comments

Optimality:
Multipliers

Review of Smooth
Dependence

Unconstrained
Controls

Excursion into
the Calculus of Variations

Gradient-Based
Numerical Methods

Constrained
Controls: Minimum Principle

Notes and Comments

Optimality:
Minimum-Time for Linear Systems

Existence Results

Maximum Principle
for Time-Optimality

Applications
of the Maximum Principle

Remarks on
the Maximum Principle

Additional
Exercises

Notes and Comments

Appendix: Linear
Algebra

Operator Norms

Singular Values

Jordan Forms
and Matrix Functions

Continuity
of Eigenvalues

Appendix: Differentials

Finite Dimensional
Mappings

Maps Between
Normed Spaces

Appendix: Ordinary
Differential Equations

Review of Lebesgue
Measure Theory

Initial-Value
Problems

Existence and
Uniqueness Theorem Linear Differential Equations

Stability of
Linear Equations

Bibliography

List
of Symbols

Index

Back to Eduardo Sontag's Public Homepage.