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ece604 lecture 18

# ece604 lecture 18 - Lecture 18 ECE 604 Linear Systems Doug...

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Nov. 17, 2009 Linear Systems © Douglas Looze 1 Lecture 18 ECE 604 Linear Systems Doug Looze

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Nov. 17, 2009 Linear Systems © Douglas Looze 2 Announcements Problem set 6 due Thursday Office hours None today Wednesday 3 - 5 Next week No class Tuesday
Nov. 17, 2009 Linear Systems © Douglas Looze 3 Last Time LTI realization problem Given a p × m transfer function G ( s ) Find a state variable model ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 d t t t dt t t t = + = + x Ax Bu y Cx Du ( 29 , , , A B C D such that the state variable transfer function is G ( s ) ( 29 ( 29 1 s s - = - + G C I A B D

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Nov. 17, 2009 Linear Systems © Douglas Looze 4 Minimal Smallest state order ( A , B ) controllable ( A , C ) observable Generalized SISO realizations Standard controllable realization Controllable Not guaranteed to be observable Standard observable realization Observable Not guaranteed to be controllable G n n m = g G n n p = g May not be minimal
Nov. 17, 2009 Linear Systems © Douglas Looze 5 Today Minimal MIMO realizations Markov parameters Hankel matrix Reading Rugh, Ch. 11 (p. 194+)

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Nov. 17, 2009
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ece604 lecture 18 - Lecture 18 ECE 604 Linear Systems Doug...

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