CDS270-2, Spring 2015

Mathematical Methods in Control and System Engineering

Instructors: Ivan Papusha, Richard M. Murray
Lectures: MW 1–1:55pm, 243 Annenberg
Units: 2–0–4
Office Hours: after class, or by appointment


This is the webpage for a new special topics course targeting graduate students and advanced undergraduates in engineering and applied math fields.


Course Description

The course will develop both a theoretical and a practical knowledge of Lyapunov theory and robust control as they pertain to modeling, analyzing, optimizing, and controlling dynamical systems from application areas in electrical systems, circuits, mechanical systems, robotics, and networks. We will highlight computational tools from convex optimization, particularly Linear Matrix Inequalities (LMIs) and semidefinite programming (SDP), as a unifying language in classical and modern control of linear systems. If time allows, we will make the jump to the rich area of nonlinear systems and path planning.

To fully appreciate the course material, students should have some level of mathematical sophistication, including a working knowledge of linear algebra, real analysis, and facility with MATLAB. A background in convex optimization (ACM 113) and/or control theory (CDS 112) will be helpful, but not required.


  1. Introduction

  2. Linear systems

  3. Lyapunov theory

  4. Convex optimization and duality

  5. Dynamic programming and LQR

  6. Linear matrix inequalities

  7. LMI approaches to mathbf{H}_2, mathbf{H}_infty problems

  8. Applications

  9. Numerical techniques

Additional notes


The final grade is tentatively based on


Each homework assignment consists of a combination of theoretical and computational problems, many of which can be freely chosen by the student from an ever-expanding catalog of problems.

HW Reading Catalog exercises* Solution Due
1 BV, Appendix A #1 Wed Apr 8
2 lmibook Ch1–2 #11 or CYOA Wed Apr 15
3 lmibook Ch1–2 #2 or CYOA Wed Apr 22
4 BV, Ch4–5 #4 or CYOA Wed Apr 29
5 Bertsekas, Ch1 #13 or CYOA Wed May 6
6 lmibook Ch4–6 #3 or CYOA Wed May 13
7 lmibook Ch7 #12 or CYOA Wed May 20
(drop day)
8 Davis Ch1–3 #19 or CYOA Wed May 27
(last day of class)

*CYOA: Choose your own adventure — do the assigned problem, or any other problem from the catalog that you haven't done.


All lecture notes will be provided in class and made available online. We will use material and readings adapted from the following texts: