Difference between revisions of "CDS 101/110  Linear Systems"
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Revision as of 05:20, 15 September 2008
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CDS 101/110a  Schedule  Recitations  FAQ  AM08 (errata) 
Overview
Monday: Linear TimeInvariant 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, 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
 ambode.m  Bode plot with AM unit choices
FAQ
Monday <ncl>CDS 101/110 FAQ  Lecture 41, Fall 2007</ncl> Wednesday <ncl>CDS 101/110 FAQ  Lecture 42, Fall 2007</ncl> Friday <ncl>CDS 101/110 FAQ  Lecture 43, Fall 2007</ncl> Homework <ncl>CDS 101/110 FAQ  Homework 4, Fall 2007</ncl>