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