ECE 780-T10: Multivariable Control Systems II (Spring 2019)

Syllabus Description

This course covers advanced topics in linear control theory and multivariable linear time-invariant controller design, and is intended primarily for graduate students in engineering and applied mathematics interested in dynamics and control. The course material is drawn from the broad area of robust control, with an emphasis on modern convex optimization approaches to robust stability/performance certification and optimal controller synthesis. Students will learn the fundamental theoretical concepts underlying robust control theory, and will be exposed to the computational frameworks used for robust stability analysis and robust controller design. Topics (subject to change) include:

  • historical context and motivation for robust control;

  • state-space LTI systems: review, Lyapunov equations, Gramians;

  • input-output LTI systems: signal spaces, rational function spaces, signal and system norms;

  • linear matrix inequalities (LMIs) and semidefinite programming;

  • the Kalman-Yakubovich-Popov (KYP) Lemma and dissipative systems theory;

  • the generalized plant framework for feedback control;

  • H-Infinity and H-2 performance analysis of control systems;

  • statement and LMI solutions of H-Infinity and H-2 control problems;

  • uncertainty modelling, robust stability/performance analysis via integral quadratic constraints;

A complete syllabus is here.


Graduate-level LTI systems theory (ECE 682 or equivalent) is strongly recommended. Exposure to optimization theory (e.g., ECE/CO 602 or equivalent) is recommended but is not required.

Lectures and Office Hours

Lecture: Mondays, 8:30am to 11:20am, EIT 3141

Office Hours: By appointment (or just drop by)


J. W. Simpson-Porco. Robust Feedback Systems and Integral Quadratic Constraints (available here)


There will be two to three assignments. Collaboration is permitted, but the submitted work must be your own. Assignments will be graded for completeness, clarity of thought, and clarity of presentation. Printed solutions will be distributed in class.

  • Note: Some assignment questions may ask you to provide formal mathematical proofs for given statements. A useful introduction to mathematical logic and proof techniques can be found here.

Final Exam

The final exam will be a 48 hour take-home final exam, at a date to be determined. Students are expected to work independently on the final exam.