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

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* MATLAB code: {{cds101 matlab|L4_1_linsys.m}}
 
* MATLAB code: {{cds101 matlab|L4_1_linsys.m}}
  
'''Wednesday:''' Linear Systems Analysis ([http://www.cds.caltech.edu/~macmardg/cds110a-fa08/L3-2_linsys.pdf Notes],  {{cds101 mp3 placeholder|cds101-2007-10-24.mp3|MP3}})
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'''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}})
  
 
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.

Revision as of 22:03, 16 October 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.

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

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.

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>