Code covered by the BSD License

# Optimal reduced-order discrete-time LQG design

### Gerard Van Willigenburg (view profile)

16 May 2008 (Updated )

Solution of the SDOPE by repeated forward and backward iteration

pinvrd(A,tol)
function [X,flag] = pinvrd(A,tol)
%PINVRD pseudo inverse with rank deficiency detection.
%   [X,flag] = PINVRD(A) produces a matrix X of the same dimensions
%   as A' so that A*X*A = A, X*A*X = X and A*X and X*A
%   are Hermitian. The computation is based on SVD(A) and any
%   singular values less than a tolerance are treated as zero.
%   The default tolerance is MAX(SIZE(A)) * NORM(A) * EPS.
%   If A is not full rank flag=1 else flag=0
%
%   PINVRD(A,TOL) uses the tolerance TOL instead of the default.
%

%   Copyright (c) 1984-98 by The MathWorks, Inc.
%   \$Revision: 5.7 \$  \$Date: 1997/11/21 23:38:41 \$
[U,S,V] = svd(A,0);
[m,n] = size(A);
if m > 1, s = diag(S);
elseif m == 1, s = S(1);
else s = 0;
end
if nargin < 2
tol = max(m,n) * max(s) * eps;
end
r = sum(s > tol);
if r<min(m,n); flag=1; else; flag=0; end;
if (r == 0)
X = zeros(size(A'));
else
s = diag(ones(r,1)./s(1:r));
X = V(:,1:r)*s*U(:,1:r)';
end