isstable.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 [fval,lambda] = isstable(model,data)
%BILIN/ISSTABLE   Determines whether a bilinear system is stable.
%
%   ISSTABLE(M,DATA) is true if the bilinear system M satsifies a
%   "stability" condition and false if it does not.
%
%   [FVAL,LAMBDA] = ISSTABLE(M,DATA) returns FVAL = 1 if the bilinear system
%   M satsifies a "stability" condition and FVAL = 0 if it does not. LAMBDA
%   is the associated largest singular value and FVAL = 1 iff LAMBDA < 1.
%
%   M has to be given as a BILIN object and DATA is an IDDATA
%   object. DATA.InputData should contain the input data.
%
%   See also BILIN, IDDATA.
%
% 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.

if nargin < 2 | isempty(data)
  error('DATA not specified in call to BILIN/ISSTABLE.')
end

A = model.A;
N = model.N;
u = data.InputData;
u = u(:,1:size(model.B,2))';

[ra,ca]=size(A);
[ru,cu]=size(u);

Lam = zeros(cu,1);

for i=1:cu
  temp = zeros(ra,ca);
  for j=1:ru
	temp = temp+u(j,i)*N(:,(j-1)*ra+1:j*ra);
  end  
  Lam(i) = max(svd((A+temp)));
end

lambda = max(Lam);

if nargout < 1
  if lambda < 1
	disp(sprintf('The system satisfies the stability condition: Lambda = %1.2e < 1.',lambda))
  else
	disp(sprintf('The system does not satisfy the stability condition: Lambda = %1.2e >= 1.',lambda))
  end
else
  if lambda < 1
	fval = 1;
  else
	fval = 0;
  end
end

	

% *** last line of isstable.m ***