The transfer functions for the state representation of continuous time LTI system:

q̇ (t) = Aq(t) + bx(t)

y(t) = cq(t) + dx(t)

is given by

This question was previously asked in

ESE Electronics 2010 Paper 1: Official Paper

Option 1 : c (sI - A)^{-1} b + d

ST 1: General Awareness

6919

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With the knowledge of the state variable representation of a plant,

the transfer function of the plant can be determined completely as given below.

X’ = Ax + Bu → (1)

Y = Cx + Du → (2)

Apply Laplace transform, to equation (1)

S X(s) = A X(s) + B U(s)

⇒ B U(s) = (SI - A) X(s)

⇒ X(s) = (SI - A)-1 B U(s)

Now apply Laplace transform to equation (2)

Y(s) = C X(s) + D U(s)

⇒ Y(s) = C[(SI - A)-1] B U(s) + D U(s)