obmat.m

剑桥大学用于线性和双线性动力学系统辨识的工具箱

function y = obmat(A,C,i)
%OBMAT   Constructs the observability matrix with a given index.
%
%   OBMAT(A,C,k) constructs the truncated (k < n), standard (k = n) or
%      extended (k > n) observability matrix of the state-space system
%      (A,B,C,D) with n states and p outputs.
%
%   Usage:
%      Y = obmat(A,C,k)
%
%   Inputs: 
%      A := Square matrix with n rows and n columns.
%      C := Matrix with p rows and n columns.
%      k := Positive integer.
%   
%   Outputs:  
%      Y := Observability matrix with k*p rows and n columns, defined as
%
%                           [     C     ]
%                           [    C*A    ]
%              Y := O_k :=  [   C*A^2   ]
%                           [     :     ]
%                           [ C*A^(k-1) ]
%
%   See also OBSV.
%
% CUED System Identification Toolbox.
% Cambridge University Engineering Department.
% Copyright (C) 1998-2002. All Rights Reserved.

% Version 1.00, Date: 01/06/2002
% Created by H. Chen and E.C. Kerrigan.
   
[rowA,colA] = size(A);
[rowC,colC] = size(C);

if rowA ~= colA,
  error('A is not a square matrix.')
end

if colC ~= colA,
  error('The column numbers of two input matrices are not equal.')
end

if (i < 1) | (i ~= fix(i)), 
  error('k is not a positive integer.')
end

p = rowC;
n = rowA;

if i == 1,
   y = C;
else
  y = zeros(i*p,n);
  d = C;
  for j = 1:i,
	y((j-1)*p+1:j*p,:) = d;
	d = d*A;	
  end
end
   
% *** last line of obmat.m ***