function [Apar,Bpar,Cpar,Dpar]= decmpc(Q,A,B,C,D)
%
% Author: Nasser M. Abbasi, Northeastern University
%
% functionality:
%
% decompose state equation A,B,C,D into a controllable/
% and a noncontrollable one.
%
% arguments:                           
% Q: IN, The transformation matrix . this is the matrix
%    returned to you from QDECMPC.M (for controllability)
% A: IN, the A matrix of the state equation
% B: IN, the B matrix of the state equation
% C: IN, the C matrix of the state equation
% D: IN, the D matrix of the state equation
% Apar:  OUT,  Apar= PAQ
% Bpar:  OUT,  Bpar= PB
% Cpar:  OUT,  Cpar= CQ
% Dpar:  OUT,  Dpar= D
%
if(nargin ~=5)
  error('Number if argumets must be 5: Q,A,B,C,D');
end

[row,col]= size(A);
if(row~= col)
  error('A matrix supplied is not SQUARE ');
end

P= inv(Q);
Apar= P*A*Q;
Bpar= P*B;
Cpar= C*Q;
Dpar= D;