Week 5: State and Output Feedback
Overview
Monday: This lecture introduces the concept of reachability and explores the use of state space feedback for control of linear systems. Reachability is defined as the ability to move the system from one condition to another over finite time. The reachability matrix test is given to check if a linear system is reachable, and the test is applied to several examples. The concept of (linear) state space feedback is introduced and the ability to place eigenvalues of the closed loop system arbitrarily is related to reachability. A cart and pendulum system and the predator prey problem are used as examples.
Wednesday: Observability is defined and full state observers are constructed to estimate the state. The stability of observers combined with state feedback is briefly discussed.
Friday: Midterm review.Handouts
Monday (CDS 101/110)
- Monday lecture handout
- MATLAB files: L5_1_reachability, cpredprey.m
Wednesday (CDS 110 only)
- Wednesday lecture handout
- Midterm (hardcopy only)
Reading
-
K. J. Åström and R. M. Murray, Analysis and Design of Feedback Systems, Preprint, 2004. Chapter 5 . (Caltech access only).
Homework
There is no homework this week due to the midterm exam.
Additional Information