hw3 - J.M. Gon calves Winter 2004 CDS 213 - Robust Control...

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Unformatted text preview: J.M. Gon calves Winter 2004 CDS 213 - Robust Control Homework # 3 Date Given: March 4, 2004 Date Due: Optional P1. Do question 7.3, DP, p. 232. P2. Do question 7.9, DP, p. 234. Show that one such controller is K ( s ) = A + B 1 B * 1 X- B 2 B * 2 X- ( I- Y X )- 1 Y C * 2 C 2 ( I- Y X )- 1 Y C * 2- B * 2 X . Now do question 7.6, DP, p.234. P3. Let M and N be suitably dimensioned matrices and let be a structured uncertainty. Prove or disprove: 1. ( M ) = 0 = M = 0. 2. ( M 1 + M 2 ) ( M 1 ) + ( M 2 ). 3. ( M ) = | | ( M ). 4. ( I ) = 1. 5. ( MN ) ( M ) ( N ). 6. ( MN ) ( N ) ( M ). P4. 1. Let = 1 2 with i structured uncertainties. Show that M 11 M 12 M 22 = max { 1 ( M 11 ) , 2 ( M 22 ) } . 2. Let M = M 12 M 21 be a complex matrix and let = 1 2 . Show that ( M ) = p ( M 12 ) ( M 21 ) ....
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This note was uploaded on 01/04/2012 for the course APH 183b taught by Professor List during the Fall '09 term at Caltech.

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hw3 - J.M. Gon calves Winter 2004 CDS 213 - Robust Control...

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