ece604 lecture 11

ece604 lecture 11 - Lecture 11 ECE 604 State Variable...

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
Oct. 15, 2009 Linear Systems © Douglas Looze 1 Lecture 11 ECE 604 State Variable Analysis Doug Looze
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Oct. 15, 2009 Linear Systems © Douglas Looze 2 Announcements PS4 available Due next week October 22
Background image of page 2
Oct. 15, 2009 Linear Systems © Douglas Looze 3 Basis change Duality Began LTI systems Controllability Matrix ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 0 0 d t t t dt t t t = + = = + x Ax Bu x x y Cx Du Controllable if and only if Last Time
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Oct. 15, 2009 Linear Systems © Douglas Looze 4 Observable if and only if Observaability Matrix
Background image of page 4
Oct. 15, 2009 Linear Systems © Douglas Looze 5 Modal controllability Distinct eigenvalues System { } { } 1 1 , , , , λ n n v v ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 0 0 LS1 d t t t dt t t t = + = = + x Ax Bu x x y Cx Du
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Oct. 15, 2009 Linear Systems © Douglas Looze 6 Define:
Background image of page 6
Oct. 15, 2009 Linear Systems © Douglas Looze 7 Let ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 0 0 LS2 d t t t dt t t t = + = = + z z WBu z Wx y CVz Du Λ Theorem: A LTI system with distinct e- values is (C) if and only if WB has no zero rows. It is (O) if and only if CV has no zero columns.
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Oct. 15, 2009 Linear Systems © Douglas Looze 8 Today Modal controllabilty and observability Repeated eigenvalues Hautus tests Reading Rugh Ch. 9 p. 144–146, 149 Ch. 13, p. 221, 232
Background image of page 8
Oct. 15, 2009 Linear Systems © Douglas Looze 9 Theorem: Consider the LTI system (LS1) and let x ( t ) = W –1 z ( t ) where W = V
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 10
This is the end of the preview. Sign up to access the rest of the document.

This document was uploaded on 04/28/2011.

Page1 / 32

ece604 lecture 11 - Lecture 11 ECE 604 State Variable...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online