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

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(Overview)
(Overview)
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* {{cds101 handouts placeholder|L4-1_linsys_h.pdf|Lecture handout}}
 
* {{cds101 handouts placeholder|L4-1_linsys_h.pdf|Lecture handout}}
* MATLAB code: {{cds101 matlab placeholder|L4_1_linsys.m}}
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* MATLAB code: {{cds101 matlab|L4_1_linsys.m}}
  
 
'''Wednesday:''' Linear Systems Analysis ({{cds101 handouts placeholder|L4-2_linsys.pdf|Notes}},  {{cds101 mp3 placeholder|cds101-2007-10-24.mp3|MP3}})
 
'''Wednesday:''' Linear Systems Analysis ({{cds101 handouts placeholder|L4-2_linsys.pdf|Notes}},  {{cds101 mp3 placeholder|cds101-2007-10-24.mp3|MP3}})

Revision as of 21:09, 8 October 2008

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

  • K. J. Åström and R. M. Murray,, Preprint, 2006..

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.

FAQ

Monday

Wednesday

Friday

Homework