# CDS 101/110 - Dynamic Behavior

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

## Overview

**Monday:** Qualitative Analysis and Stability (Slides, MP3)

This lecture provides an introduction to stability of (nonlinear) control systems. Formal definitions of stability are given and phase portraits are introduced to help visualize the concepts. Local and global behavior of nonlinear systems is discussed, using a damped pendulum and the predator-prey problem as examples.

- Lecture handout
- MATLAB code: phaseplot.m, boxgrid.m, L3_1_stability.m, oscillator.m, pendulum.m, predprey.m

**Wednesday:** Stability Analysis using Lyapunov Functions (Notes, MP3)

Lyapunov functions are introduced as a method of proving stability for nonlinear systems. Simple examples are used to explain the concepts.

- Lecture notes

**Friday:** Recitations

## Reading

- K. J. Åström and R. M. Murray, Feedback Systems: An Introduction for Scientists and Engineers, Preprint, 2007. Chapter 4 - Dynamic Behavior.

## Homework

This homework set covers stability and performance through a series of application examples. The first problem provides a set of three real-world models in which the student must identify the equilibrium points and determine stability of the equilibrium points (through simulation). The second problem explores performance specification in the conext of the cruise control example, including step response and frequency response.

## FAQ

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