ece604 lecture 05

ece604 lecture 05 - Sept. 22, 2009 Linear Systems Douglas...

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Unformatted text preview: Sept. 22, 2009 Linear Systems Douglas Looze 1 Lecture 5 ECE 604 State Variable Analysis Doug Looze Sept. 22, 2009 Linear Systems Douglas Looze 2 Announcements PS1 available Due next Thursday Office hours Today, 45 pm Tomorrow, 24 pm Sept. 22, 2009 Linear Systems Douglas Looze 3 Last Time Change of basis Self commuting ( 29 ( 29 ( 29 ( 29 Assume t t = A A A A Then ( 29 ( 29 ( 29 ( 29 ( 29 1 1 t t t t t t d d = A A A A Sept. 22, 2009 Linear Systems Douglas Looze 4 Solve directly Symbolically in terms of IC x n linearly independent ICs to obtain n solutions x i ( t ) ( 29 ( 29 ( 29 1 n t t t = X x x L is a fundamental matrix Sept. 22, 2009 Linear Systems Douglas Looze 5 Time-Invariant Systems ( 29 ( 29 ( 29 d t t dt = = x Ax x x Basis change 1 1 t t e e-- = A P AP P P Exponential formula (power series) 1 ! t k k k e t k = = A A ( 29 ( 29 t t = z Px Sept. 22, 2009 Linear Systems Douglas Looze 6 Laplace transform ( 29 { } 1 1 t e L s-- =- A I A Sept. 22, 2009 Linear Systems Douglas Looze 7 Today Discrete-time state variable models Review Reading Ch. 2021 Sept. 22, 2009Sept....
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ece604 lecture 05 - Sept. 22, 2009 Linear Systems Douglas...

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