Re: Good controls/signals text

All,

Thanks for the recommendations, but the answers were not quite what I
was looking for. I think I didn't ask the question correctly. Let me
start again.

I'm considering writing a hypertext control  / linear systems /
dynamics "text". As you know, the subject is fairly involved and
depends on a significant volume of mathematics: differential
equations, complex variables, linear algebra, transform / distribution
theory, and physics. There's really no obvious way to introduce all
these subjects to the beginning student (unlike, say calculus, which
has a pretty standard pedagogical hierarchy of e.g. functions, limits,
derivatives, integrals). As a result, most texts simply introduce the
Laplace transform out of nowhere, then try to convince the student how
useful it is. My idea is to better motivate the subject by introducing
the concept that complex exponentials are the eigenfunctions of LTI
systems, along with the analogy between signals and (infinite
dimensional) vectors (after discussing what eigenvectors and
eigenvalues are for matricies). Hence I think the Laplace transform is
nothing more than the dot product of a signal (or system) with the
complex exponential basis function. The Shaum's outline book of
Signals and Systems has some of this view. Siebert's Circuits Signals
and Systems (my prof way back when) also has some of this flavor in an
appendix, but neither book quite goes into sufficient detail. (BTW I
think the hyper linked format will work nicely to allow the student to
bring in the math as necessary.) Anyway, I'm looking for a treatment
with this "vector space" emphasis. I think, if done correctly, that
this approach might have a more intuitive feel.

Here's an example of the kind of thing I'm going for. Have you noticed
that most linear algebra (and controls) texts define the determinant
of a matrix by the procedure used to compute it, without ever really
mentioning what it IS. If you view the matrix equation y = Ax as an n-
dimensional transformation from the "x" space to the "y" space, the
determinant is just the ratio of n-dimensional volume or area between
the two spaces. That's my concept - to provide an intuitive (if not
necessarily mathematically rigorous) explanation of what things "are",
rather than just how to calculate them.

Thanks again.
Roy