The following difference equation models a discrete-time control system: y(k + 3) - yk + 2) + y(k +1)+2 y(k)=u(k) - y(k+1) - 2 y(k+2)

The following difference equation models a discrete-time control system:

y(k + 3) - yſk + 2) + y(k +1)+2 y(k)=u(k) - y(k+1) - 2 y(k+2)

where u(k) is the input. Let the output be c(k)= y(k+1).

(i) Define state variables and find a state-space representation for the system.

(ii) Determine the transfer functions C(z)/U(z) where C(z) and U(z) are the Z-transforms of c(k) and u(k), respectively.