On generalized predictive control: Two alternative formulations

-Two alternative solutions to the generalized predictive control (GPC) design problem are given for the case when the output horizon is larger than or equal to the plant order. First, using multirate models of the discrete-time plant, we present a state-space solution that does not require state observers or Riccati equation iterations for its implementation. Second, it is shown, via simple algebraic manipulations, that the key prediction equation used for GPC can be easily derived from the transfer function coefficients effectively replacing the Diophantine equation recursions by the inversion of a lower triangular matrix.