Feedback systems

Often we are interested in finding and characterizing the evolution of patterns over time. This course introduces formal tools to design, model, and analyze evolving interconnected systems in which information, data sensing, and decision-making mechanisms strongly couple two or more subsystems. Formal techniques include frequency-domain and time-domain methods.

The alternative to deterministic predictability,  when it comes unachievable,  comes from feedback…Jeff G. Bohn


Instructor: Jorge Finke

Office hours: Mondays 2:00pm – 4:00pm

Level: undergraduate

TA: Kevin Diaz

Labs: Fridays, 9:00-11:00am


Date (week staring…)Lectures (Mondays)Recitations (Wednesdays)Labs (Fridays)
Jan 20 (week 1)Lec 1 - Intro to feedback systems
Jan 27 (week 2)Lec 2 - Dynamics and modeling
Feb 3 (week 3)Lec 3 - Stability and performance
Feb 10 (week 4)Lec 4 - Lyapunov stability theoryQuiz 1
Feb 17 (week 5)Lec 5 - Lasalle theoremLab 1
Feb 24 (week 6)Lec 6 - LinearizationQuiz 2
Mar 2 (week 7)Lec 7 - State feedbackLab 2
Mar 9 (week 8)Lec 8 - Output feedbackQuiz 3
Mar 16 (week 9)——Midterm review
Mar 23 (week 10)——spring break——
Mar 30 (week 11)Lec 9 - Transfer functionsLab 3
Apr 6 (week 12)Lec 10 - Frequency domain design
Apr 13 (week 13)Lec 11 - Nyquist plotsQuiz 4Lab 4
Apr 20 (week 14)Lec 12 - PID controlers
Apr 27 (week 15)Lec 13 - PID controlersLab 5
May 4 (week 16)Lec 14 - System identificationFinal course review

 If you taking this course for credit, please fill out this form. After registering,  login and click on “enroll for this course.” You should  now be able to submit homework solutions online. Quizzes will be based on homework problems.


To access the problem sets and lab assignments please use the password provided in class. 


Dynamics and modeling

What a is a dynamic model? What does a model say about a system? Define concepts of state, dynamics, inputs and outputs. Non-linear vs. linear systems; overview modeling techniques.

Lasalle theorem

Krasovskii-Lassale Invariance Principle; Lyapunov functions for linear systems.


Compute linearization of a nonlinear system around an equilibrium point; Lyapunov Indirect Method; Examples.

State feedback

Define reachability of a system; test for reachability of linear systems; state feedback for linear systems

Output feedback

Define observability; conditions for linear systems; state estimation; examples.

Transfer functions

Content: Transfer function; Routh-Hurwitz criterion; Canonical form realizations

PID (part 1)


PID (proportional–integral–derivative controller); basic properties; PID implementation.

Course review


Validation of linear time-invariant models using barrier certificates