Question: Let the transfer function of a system be Show that by defining the state-variables as v 1 (t) = y(t),v 2 (t)=Ë y(t) + a

Let the transfer function of a system be

Y (s) bo + bịs H(s) X(s) ao + a¡s+ s²

Show that by defining the state-variables as

v₁(t) = y(t),v₂(t)=Ë™ y(t) + a₁y(t) ˆ’ b₁x(t)

we obtain a minimal state variable and output realization (i.e., only two integrators are needed). Show the matrices/vectors for the state and the output equations. Draw a block diagram for the realization.

Y (s) bo + bịs H(s) X(s) ao + a¡s+ s²

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