function [RO] = ltiro(A,C)
%
% author: Nasser M. Abbasi  
% change history
% -----------------------------------------------
% date      reason
% 3-2-92    intial
%
% -----------------------------------------------
% 
% specification: construct the observability matrix
% Ro for a time-invariant dynamic equation
%
% paramters:
% A  : is an IN argument , the nXn matrix  of state quation
% C  : is an IN argument , the C matrix of the state equation
% Ro : is an OUT parameter, the observability matrix
%
% implicit input:
% none
%
% implicit output :
% none
%
%------------------------------------------------

if(nargin ~= 2)
  error('number of input arguments must be 2, the A,C matrices');
end

[row,col]= size(A);
if(row ~= col)
  error('A matrix supplied must be a square matrix');
end

n= max(size(A));

[row,col]= size(C);

%
% build the first element of Ro
%
t(1:row,1:col)= C;

cur_row= row;
cur_col= col;
%
% Now loop from 1 to n-1 to build the rest of Rc 
%
for i=1:n-1
    a= C * A^i;
    [row,col]= size(a);
    t(cur_row+1:cur_row+row, 1:cur_col)= a;
    cur_row= cur_row+row;
end
RO= t;