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hw4-problem4

# hw4-problem4 - Let us compute the transfer function...

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(7) O (5) (3) O O O (6) O (1) O O (2) (4) O with('linalg'): A:=matrix(3,3,[1, -1, 1, 1, -2, 1, 0, -1, 0]); A d 1 K 1 1 1 K 2 1 0 K 1 0 B:=matrix(3,1,[0,1,1]); B d 0 1 1 C:=matrix(1,3,[-1,2,-1]); C d K 1 2 K 1 eigenvalues(A); 0, 0, K 1 jordan(A); 0 1 0 0 0 0 0 0 K 1 The system is not internally stable. The equilibrium at the origin is UNSTABLE (the Jordan block corresponding to the eigenvalues at the origin has dimension 2). The other eigenvalue is at -1
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Unformatted text preview: Let us compute the transfer function: W:=multiply(C,multiply(inverse(matadd(diag(s,s,s),-A)),B)); W d 2 s K 1 C 1 C 2 C 1 C K 1 2 C 1 K 2 C K 1 2 C 1 simplify(W); 1 C 1 The system is externally stable: the transfer function has only one pole at -1...
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