# Introduction to Linear Dynamical Systems

## CMPE 240 - Introduction to Linear Dynamical Systems

Please use the Forum for Questions.

Background

Linear Dynamical Systems (sometimes also called Linear Operator Theory refers to a mathematical representation of a physical system that can be represented by a set of 1st order differential equations or 1st order difference (or recursion) equations for discrete time systems. Generally, these systems can be written in a very simple (and very overloaded form) of:

The study of these linear systems started historically in the 1960's and required a Ph.D. in math as a necessary prerequisite. Most of the applications at the time were to aerospace control problems (such as rocket guidance). Today, these types of systems are studied extensively, and applications range from controls to economics. Frequently, these problems are cast as dual problems: design (where the input vector is altered to reach a desired output) and estimation(where a set a sensor measurements are processed to estimate the state of the system).

### Prerequisites

The only prerequisites for this class are exposure to Linear Algebra and Differential Equations (AMS/ENG 27 fulfills these just fine). A class on circuits (EE 70), controls (EE 154/241), signals and systems (EE 103), and/or dynamics (PHYS 5/6) would be useful, but are by no means critical. The only other prerequisites are a willingness to do the work, which will be hard at times.

Acknowledgements

This course is based on the Introduction to Linear Dynamical Systems sequence (EE263 and EE363), offered at Stanford by Professor Stephen Boyd. Lecture notes are taken from his published lecture notes, "EE263: Introduction to Linear Dynamical Systems," Fall 2004.

I would like to acknowledge the tremendous help and generosity of Prof. Stephen Boyd of Stanford University for making his instructional materials available to the wider academic world.

General Class Information

Lecture times: Tuesday-Thursday, 12:00 - 1:45 PM, Porter College Room #250

Class Webforum: WebForum - for announcements, general discussion, and help

Textbooks: note that these are NOT required, but are excellent references

Linear Algebra and its Applications, 3rd Ed. by Gilbert Strang, Brooks Cole, 1988. ISBN: 0155510053.

Teaching Assistants: TBD (unlikely to be any)