Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

Recitations: 1 session / week, 1 hour / session

Course Objectives

The course addresses dynamic systems, i.e., systems that evolve with time. Typically these systems have inputs and outputs; it is of interest to understand how the input affects the output (or, vice-versa, what inputs should be given to generate a desired output). In particular, we will concentrate on systems that can be modeled by Ordinary Differential Equations (ODEs), and that satisfy certain linearity and time-invariance conditions.

We will analyze the response of these systems to inputs and initial conditions. It is of particular interest to analyze systems obtained as interconnections (e.g., feedback) of two or more other systems. We will learn how to design (control) systems that ensure desirable properties (e.g., stability, performance) of the interconnection with a given dynamic system.

Course Outline

The course will be structured in several major sections:

1. A review of linear algebra, and of least squares problems.
2. Representation, structure, and behavior of multi-input, multi-output (MIMO) linear time-invariant (LTI) systems.
3. Robust stability and performance. Approaches to optimal and robust control design.

Hopefully, the material learned in this course will form a valuable foundation for further work in systems, control, estimation, identification, signal processing, and communications.

Assignments

Homework

Generally handed out every Wednesday, and due in class a week later (except as noted on schedule), at which time solutions will be handed out.

Tests

There will be two exams: a take-home midterm exam issued in Lecture 13 and due two days later, and a final exam during final exam week.

Grading

The course grade will depend on: (a) your involvement in the subject (30%), as evidenced mainly by your homework, but also by your interaction with the TAs and instructor; (b) your performance on the midterm exam (30%), and the final exam (40%).

Notes and Texts

The course notes are required, and are available in the Readings section.

Other texts that you may wish to examine at some point are:

Luenberger, David. Introduction to Dynamic Systems: Theory, Models, and Applications. Wiley, 1979. ISBN: 9780471025948.

Kailath, Thomas. Linear Systems. Prentice Hall, 1980. ISBN: 9780135369616.

Doyle, John, Bruce Francis, and Allen Tannenbaum. Feedback Control Theory. Dover, 2009. ISBN: 9780486469331.

Vaccaro, Richard. Digital Control: A State-Space Approach. McGraw-Hill, 1995. ISBN: 9780070667815.