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System Models

Consider the system modeled by:

x' = Ax + Bu , y = Cx + Du

where dim x=2 and dim u = dim y = 1

a) Given u=0 and the initial-state responses

1
x(0) =  y(t) = e-t− 0.5e-2t
0.5

-1
and x(0) =  y(t) = − 0.5 e-t − e-2t
1

2
Find the Initial state response for x(0) =
0.5

b) Suppose that u is a unit step input

1
x(0) =  y(t) = 0.5− 0.5e-t + e-2t
1

2
and x(0) =  y(t) = 0.5 − e-t + 1.5e-2t
2

Find y(t) when u is a unit step and x(0) = 0

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