(a) A control plant is described by the following state-space equation [x₂(k+1)] _ _[x₂(k)], [x₂(k+1)] [x₂(k) 3-4 +Bu(k) 3(k)=(√x₁(k)] [x₂(k)] -0.5]. B-[025]. C= [11].D-0 with A= -0.25 0 +Du(k), i) Find the transfer function of the plant P(z) from input u to output y. ii) What are the eigenvalues of A?

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2) (a) A control plant is described by the following state-space equation
[x₂(k+1)] [x₁(k)]
[x₂(k+1)]¯¯ [x₂(k)]
y(k)=[x,(k)] + Du(k).
-[-%
0
ii)
with A=
-0.25
+ Bu(k)
-0.5]. B-[035]. C=₁
{].C=[1_1],D=0
B=
i)
Find the transfer function of the plant P(z) from input u to output y.
What are the eigenvalues of A?
Transcribed Image Text:2) (a) A control plant is described by the following state-space equation [x₂(k+1)] [x₁(k)] [x₂(k+1)]¯¯ [x₂(k)] y(k)=[x,(k)] + Du(k). -[-% 0 ii) with A= -0.25 + Bu(k) -0.5]. B-[035]. C=₁ {].C=[1_1],D=0 B= i) Find the transfer function of the plant P(z) from input u to output y. What are the eigenvalues of A?
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