# CDS 101/110 - State Feedback

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CDS 101/110a | Schedule | Recitations | FAQ | AM08 (errata) |

## Overview

**Monday:** Reachability and State Feedback (Slides, MP3)

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.

- Lecture handout
- MATLAB code: L5_1_reachability.m, predprey.m, predprey_rh.m

**Wednesday:** State Feedback Design (MP3)

This lecture will present more advanced analysis on control using state feedback. The material from this lecture will not be covered on the homework.

- Midterm: available in class or outside 102 Steele

**Friday:** Midterm review (sorry, forgot to press 'record' on MP3 recorder)

- Midterm review notes Note: the plots at the end show the example problem before (unstable) and after (stable) applying state feedback.

## Reading

- K. J. Åström and R. M. Murray, Feedback Systems: An Introduction for Scientists and Engineers, Preprint, 2007. Chapter 6 - State Feedback.

## Midterm

The exam will consist of 3-5 problems, covering the material in the first five weeks of the course (including reachability and state feedback). The exam will be open book. You may use the course notes, any of the optional texts (Friedland, Franklin-Powell and Emami-Naeni, Lewis), course handouts, lecture notes, course problem sets and solutions, and your own handwritten notes. *No other books are allowed.*

You may use a computer or calculator for carrying out *numerical* computations. MATLAB may be used but is not required. You are not allowed to use the Internet during the exam (except for accessing local computing resources, such as MATLAB/SIMULINK), but you may download or print out copies of presentations, notes, FAQs, or other material posted on the course web site (CDS 101 or 110). You are not allowed to print out contents of other sites for use while taking the exam (although you can take handwritten notes on the sites and use your own notes in the exam).

The exam will be due by 5 p.m. Tuesday, 6 November, in the box outside 102 Steele. Please write your solutions in a fresh exam book (blue book). We have to grade a large collections of exams in a short time and it makes things much simpler to manage if everyone uses a bluebook.

## FAQ

**Monday**
<ncl>CDS 101/110 FAQ - Lecture 5-1, Fall 2007</ncl>
**Wednesday**
<ncl>CDS 101/110 FAQ - Lecture 5-2, Fall 2007</ncl>
**Friday**
<ncl>CDS 101/110 FAQ - Lecture 5-3, Fall 2007</ncl>
**Midterm**
<ncl>CDS 101/110 FAQ - Midterm, Fall 2007</ncl>