# Difference between revisions of "CDS 101/110 - Linear Systems"

Line 1: | Line 1: | ||

− | {{cds101- | + | {{cds101-fa07}} |

{{righttoc}} | {{righttoc}} | ||

== Overview == | == Overview == | ||

− | '''Monday:''' Linear Time-Invariant Systems ({{cds101 handouts|L4- | + | '''Monday:''' Linear Time-Invariant Systems ({{cds101 handouts|L4-1_linsys.pdf|Slides}}, {{cds101 mp3 placeholder|cds101-2007-10-22.mp3}}) |

This lecture gives an introduction to linear input/output systems. The main properties of linear systems are given and the matrix exponential is used to provide a formula for the output response given an initial condition and input signal. Linearization of nonlinear systems as an approximation of the dynamics is also introduced. | This lecture gives an introduction to linear input/output systems. The main properties of linear systems are given and the matrix exponential is used to provide a formula for the output response given an initial condition and input signal. Linearization of nonlinear systems as an approximation of the dynamics is also introduced. | ||

− | '''Wednesday:''' Linear Systems Analysis ({{cds101 handouts|L4-2_linearization.pdf|Notes}}, | + | * {{cds101 handouts|L4-1_linsys_h.pdf|Lecture handout}} |

+ | * MATLAB code: {{cds101 matlab|L4_1_linsys.m}} | ||

+ | |||

+ | '''Wednesday:''' Linear Systems Analysis ({{cds101 handouts placeholder|L4-2_linearization.pdf|Notes}}, {{cds101 mp3 placeholder|cds101-2007-10-24.mp3}}) | ||

Further analysis of linear systems, including a derivation of the convolution integral and the use of Jordan form. This lecture also covers the use of linearization to approximate the dynamics of a nonlinear system by a linear system. | Further analysis of linear systems, including a derivation of the convolution integral and the use of Jordan form. This lecture also covers the use of linearization to approximate the dynamics of a nonlinear system by a linear system. | ||

+ | * {{cds101 handouts placeholder|L4-2_linearization.pdf|Lecture notes}} | ||

− | '''Friday:''' | + | '''Friday:''' [[CDS 101/110, Fall 2007 - Recitation Schedule|recitations]] |

− | |||

− | |||

− | |||

− | |||

− | |||

− | |||

− | |||

− | |||

− | |||

− | |||

− | |||

− | |||

− | |||

− | |||

− | | | ||

== Reading == | == Reading == | ||

Line 35: | Line 24: | ||

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

− | This homework set covers linear control systems. The first problem asks for stability, step and frequency response for some common examples of linear systems. The second problem considers stabilization of an inverted pendulum on a cart, using the local linaerization. The remaining problems (for CDS 110 students) include derivation of discrete time linear systems response functions | + | This homework set covers linear control systems. The first problem asks for stability, step and frequency response for some common examples of linear systems. The second problem considers stabilization of an inverted pendulum on a cart, using the local linaerization. The remaining problems (for CDS 110 students) include Lypunov functions for linear systems and derivation of discrete time linear systems response functions. |

<!-- Links to homework materials --> | <!-- Links to homework materials --> | ||

* {{cds101 handouts|hw4.pdf|Homework #4}} | * {{cds101 handouts|hw4.pdf|Homework #4}} | ||

− | * {{cds101 matlab| | + | * {{cds101 matlab|balance_simple.mdl}} - SIMULINK model of a balance system |

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

'''Monday''' | '''Monday''' | ||

− | <ncl>CDS 101/110 FAQ - Lecture 4-1</ncl> | + | <ncl>CDS 101/110 FAQ - Lecture 4-1, Fall 2007</ncl> |

'''Wednesday''' | '''Wednesday''' | ||

− | <ncl>CDS 101/110 FAQ - Lecture 4-2</ncl> | + | <ncl>CDS 101/110 FAQ - Lecture 4-2, Fall 2007</ncl> |

'''Friday''' | '''Friday''' | ||

− | <ncl>CDS 101/110 FAQ - Lecture 4-3</ncl> | + | <ncl>CDS 101/110 FAQ - Lecture 4-3, Fall 2007</ncl> |

'''Homework''' | '''Homework''' | ||

− | <ncl>CDS 101/110 FAQ - Homework 4</ncl> | + | <ncl>CDS 101/110 FAQ - Homework 4, Fall 2007</ncl> |

## Revision as of 15:08, 22 October 2007

WARNING: This page is for a previous year.See current course homepage to find most recent page available. |

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

## Overview

**Monday:** Linear Time-Invariant Systems (Slides, {{{2}}})

This lecture gives an introduction to linear input/output systems. The main properties of linear systems are given and the matrix exponential is used to provide a formula for the output response given an initial condition and input signal. Linearization of nonlinear systems as an approximation of the dynamics is also introduced.

- Lecture handout
- MATLAB code: L4_1_linsys.m

**Wednesday:** Linear Systems Analysis (Notes, {{{2}}})

Further analysis of linear systems, including a derivation of the convolution integral and the use of Jordan form. This lecture also covers the use of linearization to approximate the dynamics of a nonlinear system by a linear system.

- Lecture notes

**Friday:** recitations

## Reading

- K. J. Åström and R. M. Murray, Feedback Systems: An Introduction for Scientists and Engineers, Preprint, 2006. Chapter 5 - Linear Systems.

## Homework

This homework set covers linear control systems. The first problem asks for stability, step and frequency response for some common examples of linear systems. The second problem considers stabilization of an inverted pendulum on a cart, using the local linaerization. The remaining problems (for CDS 110 students) include Lypunov functions for linear systems and derivation of discrete time linear systems response functions.

- Homework #4
- balance_simple.mdl - SIMULINK model of a balance system

## FAQ

**Monday**
<ncl>CDS 101/110 FAQ - Lecture 4-1, Fall 2007</ncl>
**Wednesday**
<ncl>CDS 101/110 FAQ - Lecture 4-2, Fall 2007</ncl>
**Friday**
<ncl>CDS 101/110 FAQ - Lecture 4-3, Fall 2007</ncl>
**Homework**
<ncl>CDS 101/110 FAQ - Homework 4, Fall 2007</ncl>