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

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− | {{ | + | {{cds101-fa08 lecture|prev=Dynamic Behavior|next=State Feedback}}__NOTOC__ |

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

− | '''Monday:''' Linear Time-Invariant Systems ({{cds101 handouts|L4-1_linsys.pdf|Slides}}, {{cds101 mp3|cds101- | + | '''Monday:''' Linear Time-Invariant Systems ({{cds101 handouts placeholder|L4-1_linsys.pdf|Slides}}, {{cds101 mp3|cds101-2008-10-13.mp3|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. | ||

− | * | + | * [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/L3-1_linsys.pdf Lecture handout] |

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

− | '''Wednesday:''' Linear Systems Analysis ( | + | '''Wednesday:''' Linear Systems Analysis ([http://www.cds.caltech.edu/~macmardg/cds110a-fa08/L3-2_linsys.pdf Notes], {{cds101 mp3|cds101-2008-10-15.mp3.mp3|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. | ||

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

− | * {{ | + | * {{AM08|Chapter 5 - Linear Systems}} |

== 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 | + | 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 linearization. The remaining problems (for CDS 110 students) include derivation of discrete time linear systems response functions. |

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

− | * {{cds101 handouts placeholder| | + | <!--* {{cds101 handouts placeholder|hw3.pdf|Homework #3}} --> |

− | * | + | * [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/hw3-101-fa08.pdf hw3 - 101] |

+ | * [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/hw3-110-fa08.pdf hw3 - 110] | ||

+ | * [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/hw3-210-fa08.pdf hw3 - 210] | ||

+ | * [http://www.cds.caltech.edu/~macmardg/cds110a-fa08/balance_simple.mdl balance_simple.mdl] - SIMULINK model of a balance system | ||

* [[Media:Ambode.m|ambode.m]] - Bode plot with AM unit choices | * [[Media:Ambode.m|ambode.m]] - Bode plot with AM unit choices | ||

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

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

− | <ncl>CDS 101/110 FAQ - Lecture | + | <ncl>CDS 101/110 FAQ - Lecture 3-1, Fall 2008</ncl> |

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

− | <ncl>CDS 101/110 FAQ - Lecture | + | <ncl>CDS 101/110 FAQ - Lecture 3-2, Fall 2008</ncl> |

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

− | <ncl>CDS 101/110 FAQ - Lecture | + | <ncl>CDS 101/110 FAQ - Lecture 3-3, Fall 2008</ncl> |

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

− | <ncl>CDS 101/110 FAQ - Homework | + | <ncl>CDS 101/110 FAQ - Homework 3, Fall 2008</ncl> |

## Latest revision as of 05:56, 9 December 2008

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

## Overview

**Monday:** Linear Time-Invariant Systems (Slides, 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.

- Lecture handout
- MATLAB code: L4_1_linsys.m

**Wednesday:** Linear Systems Analysis (Notes, 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.

- Lecture notes

**Friday:** recitations

## Reading

- K. J. Åström and R. M. Murray, Feedback Systems: An Introduction for Scientists and Engineers, Princeton University Press, 2008. 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 linearization. The remaining problems (for CDS 110 students) include derivation of discrete time linear systems response functions.

- hw3 - 101
- hw3 - 110
- hw3 - 210
- balance_simple.mdl - SIMULINK model of a balance system
- ambode.m - Bode plot with AM unit choices

## FAQ

**Monday**
<ncl>CDS 101/110 FAQ - Lecture 3-1, Fall 2008</ncl>
**Wednesday**
<ncl>CDS 101/110 FAQ - Lecture 3-2, Fall 2008</ncl>
**Friday**
<ncl>CDS 101/110 FAQ - Lecture 3-3, Fall 2008</ncl>
**Homework**
<ncl>CDS 101/110 FAQ - Homework 3, Fall 2008</ncl>