What Background Is Needed For Control Theory?

[camdenreslink]

I'm an engineering major, and my school has a lab that works on control theory. I think I would like to work on this in grad school, but I don't know if I have the background to look into it yet?

I found a free textbook on the subject from Rutgers:
http://www.math.rutgers.edu/~sontag/FTP_DIR/sontag_mathematical_control_theory_springer98.pdf"

I've only studied Calc I-III thus far. Linear Algebra isn't required for my degree, and I only need to take a "Intro to Diff. EQs" class, which I'm guessing is pretty lightweight.

What am I going to have to study to be able to understand material in a textbook like this?
- Diff Equations?
- Linear Algebra?
- Real/Complex/Functional Analysis?
- Abstract Algebra?
- Geometry/Topology?

The textbook preface says that only linear algebra and diff equations are required, but I'm skeptical.

 

[chingkui]

Looks to me like you need to know (and be very good at) Diff Equations, Linear Algebra, Real and Functional Analysis to understand that book. Most engineers do not approach the subject from a rigorous mathematical point of view though, and certainly would not use the book you mentioned to learn it.

In any case, if you want to learn control system, you definitely need to be very good at linear algebra, and the intro to linear algebra most school offer will not be enough, got to be a bit more rigorous and abstract. If you like to be more theoretical, then analysis is a must.

"Linear System Theory and Design" by Chi-Tsong Chen is a much better book to read than Sontag's book for an engineer, although it will still be painful if you approach the subject for the first time. Can't think of a better one though...