predict_mats.m

function [F,G] = predict_mats(A,B,N)
%
% PREDICT_MATS.M returns the MPC prediction matrices for a system
%
%	x^+ = A*x + B*u
%
% That is, the matrices F and G from the equation
%
%	X = F*x + G*U
%
% USAGE:
%
% 	[F,G] = predict_mats(A,B,N)
%
% where N is prediction horizon length.
%
% P. Trodden, 2015.

% dimensions
n = size(A,1);
m = size(B,2);

% allocate
F = zeros(n*N,n);
G = zeros(n*N,m*(N-1));

% form row by row
for i = 1:N
   %  F
   F(n*(i-1)+(1:n),:) = A^i;
   
   % G
   % form element by element
   for j = 1:i
       G(n*(i-1)+(1:n),m*(j-1)+(1:m)) = A^(i-j)*B;
   end
end