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Let the state-space representation of an LTI system be ̇x(t)=A x(t)+B u(t), y(t)=C x(t)+d u(t) where A, B, C are matrices, d is a scalar, u(t) is the input to the system, and y(t) is its output. Let B=[0 0 1]T and d=0. Which one of the following options for A and C will ensure that the transfer function of this LTI system is H(s)=1/(s3+3s2+2s+1)?
A
A=[[0,1,0],[0,0,1],[-1,-2,-3]] and C=[1,0,0]
B
A=[[0,1,0],[0,0,1],[-3,-2,-1]] and C=[1,0,0]
C
A=[[0,1,0],[0,0,1],[-1,-2,-3]] and C=[0,0,1]
D
A=[[0,1,0],[0,0,1],[-3,-2,-1]] and C=[0,0,1]

Correct : a

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