ece604 lecture 07

ece604 lecture 07 - Sept 29 2009 Linear Systems © Douglas...

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Unformatted text preview: Sept. 29, 2009 Linear Systems © Douglas Looze 1 Lecture 7 ECE 604 State Variable Analysis Doug Looze Sept. 29, 2009 Linear Systems © Douglas Looze 2 Announcements PS2 available – Due Thursday Sept. 29, 2009 Linear Systems © Douglas Looze 3 Last Time Solution to state variable model – Variation of constants formula ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 , , , , t t t t t t t t d t t t t t t d t t σ σ σ σ σ σ σ σ = + = + + ∫ ∫ x x B u y C x C B u D u Φ Φ Φ Φ Sept. 29, 2009 Linear Systems © Douglas Looze 4 Transformations of inhomogeneous linear systems State transformations Equivalence – Existence of state transformation Sept. 29, 2009 Linear Systems © Douglas Looze 5 Time-Invariant Systems Solution ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 d t t t dt t t t = + = = + x Ax Bu x x y Cx Du ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 t t t t t t t e e d t e e d t σ σ σ σ σ σ-- = + = + + ∫ ∫ A A A A x x Bu y C x C Bu Du Sept. 29, 2009 Linear Systems © Douglas Looze 6 Laplace transform ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 d t t t dt t t t = + = = + x Ax Bu x x y Cx Du ( 29 ( 29 ( 29 s s s s- = + x x Ax Bu ( 29 ( 29 ( 29 ( 29 1 1 s s s s-- =- +- x I A x I A Bu ( 29 ( 29 ( 29 ( 29 ( 29...
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ece604 lecture 07 - Sept 29 2009 Linear Systems © Douglas...

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