# CDS 101/110 - Dynamic Behavior

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## Overview

The learning objectives for this week are:

- Students should be able to use a phase portraits to describe the behavior of dynamical systems and determine the stability of an equilibrium point
- Students should be able to find equilibrium points for a nonlinear system and determine whether they are stable using linearizations (all) and Lyapunov functions (CDS 110/210)
- Students should be able to explain the difference between stability, asymptotic stability, and global stability

**Monday:** Qualitative Analysis and Stability (Slides, MP3- due to technical difficulties, this is last year's lecture)

- 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, L2_1_stability.m, oscillator.m, invpend.m, predprey.m

**Wednesday:** Stability Analysis using Lyapunov Functions (Notes, MP3- due to technical difficulties, this is last year's lecture)

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

**Friday:** Recitations

## Reading

- K. J. Åström and R. M. Murray,, Princeton University Press, 2008..
- CDS 101: Read sections 4.1-4.3 [30 min]
- CDS 110: Read sections 4.1-4.4, up to Krasolvski-Lasalle (p 118) [60 min]
- CDS 210: Review sections 4.1-4.3, read sections 4.4-4.5 [60 min]

## Homework

## FAQ

**Monday**
<ncl>CDS 101/110 FAQ - Lecture 2-1, Fall 2008</ncl>
**Wednesday**
<ncl>CDS 101/110 FAQ - Lecture 2-2, Fall 2008</ncl>
**Homework**
<ncl>CDS 101/110 FAQ - Homework 2, Fall 2008</ncl>