function [X0] = getxo(a,b,c,d,u,y,DFLAG)
%GETXO Compute the initial states for a state space.
%   GETX0 is used by Linear Systems blocks in the Extras block library.
%   The blocks:
%
%     Zero-Pole with Initial States
%     Zero-Pole with Initial Outputs
%     State-Space with Initial Outputs
%     Transfer Fcn with Initial States
%     Transfer Fcn with Initial Outputs
%     Discrete Zero-Pole with Initial States
%     Discrete Zero-Pole with Initial Outputs
%     Discrete Transfer Fcn with Initial States
%     Discrete Transfer Fcn with Initial Outputs
%
%   allow you to provide initial conditions or initial outputs to Transfer
%   Function, Zero-Pole-Gain, and State Space blocks.

%   Copyright 1990-2000 The MathWorks, Inc.
%   $Revision: 1.10 $

% get the relevant matrix sizes
[m,n] = size(a);
[n,p] = size(b);
[q,n] = size(c);

%
% Build the A and B matrices for the linear programming routine
% simlp.m
%
% Note that there is a set of equality constraints set by the
% cx+du = y equations.
%
if (DFLAG == 0)
  %it is a continuous system
  A = [   zeros(q,1)    c  ;
        -1*ones(m,1)    a  ;
        -1*ones(m,1)   -a ];
else
  %  it is a discrete system
  A = [   zeros(q,1)    c  ;
        -1*ones(m,1)    (a - eye(m))  ;
        -1*ones(m,1)    (eye(m) - a) ];
end

B = [  y - d * u   ;
           b * u   ;
          -b * u  ];

%
% Now the first element of the state vector is lambda,  the slack variable
% and the rest is the x vector of the equations.
%
% So now we can do the optimization for the function f'x where
% f is a 1 followed by a zero for each state, ie f'x=lambda
%
f = [1 zeros(1,n)];
[X,lambda,how]=simlp(f(:),A,B(:),[],[],[],q,0);
X0 = X(2:length(X));
Xdot = (a*X0+b*u);
