Book recently published

[Eduardo Sontag]

The following textbook in control and systems theory may be useful to those
working on neural nets, especially if interested in recurrent nets and other
dynamic behavior.  The level is begining-graduate; it is written in a careful
mathematical style, but its contents should be accessible to anyone with a
good undergraduate-level math background including calculus, linear algebra,
and differential equations:

Eduardo D. Sontag,
__Mathematical Control Theory: Deterministic Finite Dimensional Systems__
Springer, New York, 1990. (396+xiii pages)

Some highlights:

** Introductory chapter describing intuitively modern control theory

** Automata and linear systems covered in a *unified* fashion

** Dynamic programming, including variants such as forward programming

** Passing from dynamic i/o data to internal recurrent state representations

** Stability, including Lyapunov functions

** Tracking of time-varying signals

** Kalman filtering as deterministic optimal observation

** Linear optimal control, including Riccati equations

** Determining internal states from input/output experiments

** Classification of internal state representations under equivalence

** Frequency domain considerations: Nyquist criterion, transfer functions

** Feedback, as a general concept, and linear feedback; pole-shifting

** Volterra series

** Appendix: differential equation theorems

** Appendix: singular values and related matters


** Detailed bibliography (400 up-to-date entries)
** Large computer-generated index

Some data:

Springer-Verlag, ISBN: 0-387-97366-4; 3-540-97366-4
Series: Textbooks in Applied Mathematics, Number 6.  Hardcover, $39.00
[Can be ordered in the USA from 1-800-SPRINGER (in NJ, 201-348-4033)]