ece604 lecture 14

# ece604 lecture 14 - Lecture 14 ECE 604 State Variable...

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Oct. 27, 2009 Linear Systems © Douglas Looze 1 Lecture 14 ECE 604 State Variable Analysis Doug Looze

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Oct. 27, 2009 Linear Systems © Douglas Looze 2 Announcements PS5 available Due Thursday, October 29 Midterm exam Wednesday, November 4 7–9 P.M. LGRT A203 Open book, notes No electronic devices No class Thursday, Nov. 5
Oct. 27, 2009 Linear Systems © Douglas Looze 3 Last Time Controllable canonical decomposition Define: The controllable subspace X c of the LTI system d d t x t ( 29 = A x t ( 29 + Bu t ( 29 is the subspace of states that can be reached from x (0)=0 for some admissible control. Theorem: The controllable subspace is the span of the columns of the controllability matrix

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Oct. 27, 2009 Linear Systems © Douglas Looze 4 System ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 [ ] ( 29 ( 29 ( 29 12 c c c c c c c c c c c d t t dt t t d t dt t t t t = + = + x A A x B u A x x x y C C Du x Controllable Canonical Decomposition
Oct. 27, 2009 Linear Systems © Douglas Looze 5 Theorem

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Oct. 27, 2009 Linear Systems © Douglas Looze 6 Observable canonical decomposition Define: The unobservable subspace of the LTI system ( 29 ( 29 ( 29
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ece604 lecture 14 - Lecture 14 ECE 604 State Variable...

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