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Unformatted text preview: ) is P = C z C1 x (where the C matrices are the controllability matrices for the respective systems). 7. Given ˙ x ( t ) = 2 13 22 21 x ( t ) + 1 1 u ( t ) y ( t ) = h 1 1 1 i x ( t ) for which of the following initial states is it possible to ﬁnd u ( t ), 0 ≤ t ≤ 4, so that x (4) = 0? (a) x (0) = [1 2 1] T (b) x (0) = [1 1 0] T (c) x (0) = [1 1 1] T (d) x (0) = [1 3 2] T 8. For ˙ x ( t ) = 123 1 1 x ( t ) + 1 u ( t ) y ( t ) = h 1 5 6 i x ( t ) (a) ﬁnd K (in terms of p 1 , p 2 and p 3 ) so that the poles of the v to y system achieved by u = vKx are atp 1 ,p 2 andp 3 ; (b) ﬁnd K so that the transfer function of the v to y system achieved by u = vKx is G ( s ) = 1 s + 1...
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 Spring '07
 Williamson
 LTI system theory

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