Digital Control Systems

Textbooks
- Introduction to Applied Digital Control, Greg Starr, University of New Mexico
  - Greg's ME481/ME581 web pages contain solutions to the book problems and other things.
- Optimal Sampled-Data Control Systems, Chen & Francis
- Digital Control System Analysis and Design, 3rd Ed., Philips
- Control Systems and Control Engineering
- Introduction to Signal Processing
- Zoran Gajic's Book on Control Systems (Continuous & Discrete) and some other documents. Look for the documents entitled Chapter N.
Lectures
- Sampled Time Control
- Zoran Gajic's notes on Observers. This is a very short set of lecture notes that explains the why's of observers, with several interesting derivations.
Papers
- [file:///home/frohro/Downloads/an%20introduction%20to%20observers.pdf David Luenberger's Review of Observers]

Relationship between the Laplace and Z transforms
Convolution and Z Transforms
- Z Transforms and Convolution
- Here is an animation of convolution with continuous signals. Look at it so you understand what is happening with the mechanics of convolution. To convolve $x(t)$ $x(t)$ with $h(t)$ $h(t)$ , you flip shift $h(t)$ $h(t)$ into $h(t-t_{0})$ $h(t-t_{0})$ on the $t_{0}$ $t_{0}$ axis, then you multiply it by $x(t_{0})$ $x(t_{0})$ to get $x(t_{0})h(t-t_{0})$ $x(t_{0})h(t-t_{0})$ , then you integrate with respect to $t_{0}$ $t_{0}$ , so that the convolution is: $x(t)*h(t)=\int _{-\infty }^{\infty }x(t_{0})h(t-t_{0})dt_{0}$ $x(t)*h(t)=\int _{-\infty }^{\infty }x(t_{0})h(t-t_{0})dt_{0}$ . The first animation shows this happening with sampled waveforms: $x_{s}(t)=x(t)\sum _{n=0}^{\infty }\delta (t-nT)=\sum _{n=0}^{\infty }x(nT)\delta (t-nT)$ $x_{s}(t)=x(t)\sum _{n=0}^{\infty }\delta (t-nT)=\sum _{n=0}^{\infty }x(nT)\delta (t-nT)$ and $h_{s}(t)=h(t)\sum _{n=0}^{\infty }\delta (t-nT)=\sum _{n=0}^{\infty }h(nT)\delta (t-nT)$ $h_{s}(t)=h(t)\sum _{n=0}^{\infty }\delta (t-nT)=\sum _{n=0}^{\infty }h(nT)\delta (t-nT)$ .
  - Discrete convolution animations
- Notice that this is really the same as Polynomial Multiplication.