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Unformatted text preview: EE302 HW8 Due: 28 May 2010 Q1. Consider the following system: ... y + 4¨ y + 5 ˙ y + 2 y = 5 ˙ u + u. Obtain controllable canonical, observable canonical, and (if possible) diagonal canonical state space representations. Q2. Consider the following system: ˙ x = [- 1 1 7- 7 ] x + [ 1 2 ] u y = [1 1] x. Obtain the transfer function Y ( s ) /U ( s ) and find its poles and zero(s). Obtain controllable canonical and observable canonical state space representations. Q3. Consider the following system: ˙ x = Ax + Bu y = Cx where A = [- 1 1 7- 7 ] (a) Find the eigenvalues of A . (b) Find (right) eigenvectors r 1 , r 2 ∈ R 2 × 1 of A . (c) Is system controllable for B = r 1 ? How about for B = r 2 ? (d) Find (left) eigenvectors ℓ 1 , ℓ 2 ∈ R 2 × 1 of A . (Vector ℓ is said to be a left eigenvector with corresponding eigenvalue λ if it satisfies ℓ T A = λℓ T .) (e) Is system observable for C = ℓ T 1 ? How about for C = ℓ T 2 ?...
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