# Linear Systems

ECE 717

University of Wisconsin–Madison
This is a graduate-level course on linear dynamical systems with an emphasis on state-space modeling in both discrete and continuous time. Topics covered include equilibrium points and linearization, natural and forced responses, canonical forms and transformations, controllability and observability, control-theoretic concepts such as pole placement, stabilization, dynamic compensation, and the separation principle. This course presents material that should be fundamental knowledge for students pursuing research in systems/control theory, signal processing, or mechanical/electrical/industrial engineering. The official prerequisite is MATH 340. Unofficially, you should be comfortable with linear algebra and MATLAB, and preferably have taken an introductory systems/controls course (e.g. ECE 330, 332 or 334)

**Instructor:** Laurent Lessard.

**IMPORTANT:** The notes below are from Fall 2019-20, which was the last time Prof. Lessard taught this course. More recent offerings of the course might use different notes/materials.

**Note:** Only the rows containing a date are guaranteed to be current. All other rows contain notes from the 2017-18 offering of this course (for your reference). Topics covered this year may change at my discretion.

## Part I: State-space fundamentals

## Part II: Analysis topics

## Part III: Design and feedback

## Textbook:

We will make use of the following textbook throughout the class.

**The book is freely available** and can be downloaded as a PDF as long as you’re connected to the UW network. If you’re accessing remotely, you can use

EZProxy. When the textbook does not perfectly match what we cover in class, we will provide additional supplements to the textbook.

Several other textbooks can serve as auxiliary references. For linear algebra, I recommend:

- Gilbert Strang.
*Linear algebra and its applications*.
- Sheldon Axler.
*Linear algebra done right*.

For linear systems, I recommend:

- Panos J. Antsaklis and Anthony N. Michel.
*Linear systems*.
- Chi-Tsong Chen.
*Linear system theory and design*.

You will not need these books. I’m only listing them in case you want to consult additional references.

## Coding:

You will be required to write MATLAB code to solve some of the homework problems. As a UW student, you have access to MATLAB for free via the

Campus Software Library. I will assume you have working knowledge of MATLAB for this class. That being said, you won’t be asked to code anything more complicated than simple 10-20 line scripts.