ccom(A,b,c)

function [C, O] = ccom(A,b,c)
%CCOM Canonical form Controllability and Observability Matrices
%
%Given a system described in state space by A, b, c, and d
%with a transfer function of Poly(numerator)/Poly(denominator),
%this program computes two matrices C and O such that
%   inv(C)*A*C and O*A*inv(O) generate a canonical companion form of A
%with the (-) denominator coefficients in a row or column and
%   inv(C)*b and c*inv(O) generate a canonical [0 0 ... 0 1] form and
%   c*C and O*b generate a canonical form
%containing the numerator coefficients when d=0.
%
%usage: [C, O] = ccom(A,b,c)
%
%tested with version 6.5.0.18 (R13)
%
%see also: CTRB, OBSV, ss, tf, compan, place, acker, pzplace
%

%Paul Godfrey
%March 29, 2007
%corrected a help typo

if nargin<1
   clc
   help ccom
   return
end

debug=0;

b=b(:);
c=c(:).';

n=length(A);
C=[b];
O=[c];
for k=2:n
    C=[b  A*C];
    O=[c; O*A];
end

p=poly(eig(A));
M=fliplr(triu(toeplitz(p(1:n))));
C=C*M;
O=M*O;

if debug==1
  t=tf(ss(A,b,c,0))

  inv(C)*A*C
  inv(C)*b
         c*C

  disp(' ')
  disp(' ')

  O*A*inv(O)
  O*b
    c*inv(O)
end

return