# Difference between revisions of "CDS 101/110 - Dynamic Behavior"

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'''Monday:''' Qualitative Analysis and Stability ({{cds101 handouts|L2-1_stability.pdf|Slides}}, {{cds101 mp3 placeholder|cds101-2007-10-15.mp3|MP3}}) | '''Monday:''' Qualitative Analysis and Stability ({{cds101 handouts|L2-1_stability.pdf|Slides}}, {{cds101 mp3 placeholder|cds101-2007-10-15.mp3|MP3}}) | ||

+ | <p> | ||

+ | :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. | ||

− | + | :* {{cds101 handouts|L2-1_stability_h.pdf|Lecture handout}} | |

− | + | :* MATLAB code: {{cds101 matlab|phaseplot.m}}, {{cds101 matlab|boxgrid.m}}, {{cds101 matlab|L2_1_stability.m}}, {{cds101 matlab|oscillator.m}}, {{cds101 matlab|invpend.m}}, {{cds101 matlab|predprey.m}} | |

− | * {{cds101 handouts|L2-1_stability_h.pdf|Lecture handout}} | + | </p> |

− | * MATLAB code: {{cds101 matlab|phaseplot.m}}, {{cds101 matlab|boxgrid.m}}, {{cds101 matlab|L2_1_stability.m}}, {{cds101 matlab|oscillator.m}}, {{cds101 matlab|invpend.m}}, {{cds101 matlab|predprey.m}} | ||

− | |||

'''Wednesday:''' Stability Analysis using Lyapunov Functions ({{cds101 handouts|L2-2_lyapunov.pdf|Notes}}, {{cds101 mp3 placeholder|cds101-2007-10-17.mp3|MP3}}) | '''Wednesday:''' Stability Analysis using Lyapunov Functions ({{cds101 handouts|L2-2_lyapunov.pdf|Notes}}, {{cds101 mp3 placeholder|cds101-2007-10-17.mp3|MP3}}) | ||

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

− | * {{cds101 handouts|L2-2_lyapunov.pdf|Lecture notes}} | + | :* {{cds101 handouts|L2-2_lyapunov.pdf|Lecture notes}} |

'''Friday:''' [[CDS 101/110a, Fall 2008 - Recitation Schedule|Recitations]] | '''Friday:''' [[CDS 101/110a, Fall 2008 - Recitation Schedule|Recitations]] | ||

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== Homework == | == Homework == | ||

− | * {{cds101 handouts placeholder|hw2.pdf|Homework #2}} | + | * {{cds101 handouts placeholder|hw2-fa08.pdf|Homework #2}} |

== FAQ == | == FAQ == |

## Revision as of 17:00, 5 October 2008

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

## 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)

- 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)

- 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, Feedback Systems: An Introduction for Scientists and Engineers, Princeton University Press, 2008. Chapter 4 - Dynamic Behavior.
- 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

- Homework #2

## 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>