ismpbalanced.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 = ismpbalanced(sys)
%ISMPBALANCED   True if the given system is balanced.
%
%   ISMPBALANCED(SYS) returns 1 if (A,B,C) is minimum-phase balanced and 0
%   otherwise. SYS has to be an SS or IDSS object. The system is
%   minimum-phase balanced iff the controllability gramian Wc of SYS is
%   equal to the observability gramian Wo of inv(SYS).
%
%   See also GRAM, SS, IDSS, MPBAL, BALREAL, ISBALANCED.
%
% 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 isa(sys,'idss')
  sys = ss(sys.a,sys.b,sys.c,sys.d,sys.Ts);
elseif ~isa(sys,'ss')
  error('The given system is not an SS or IDSS object.')
end

Wc = gram(sys,'c'); % Controllability Gramian of SYS
Wo = gram(inv(sys),'o'); % Observability Gramian of inv(SYS)


tol = 1e3*eps; % A small tolerance

if norm(Wc-Wo) > tol
  if nargout == 0
	disp(sprintf('System is not minimum-phase balanced; norm(Wc(SYS)-Wo(inv(SYS))) = %4.2e.',norm(Wc-Wo)))
  else
	fval = 0;
  end
else
  if nargout == 0
	disp(sprintf('System is minimum-phase balanced; norm(Wc(SYS)-Wo(inv(SYS))) = %4.2e.',norm(Wc-Wo)))
  else
	fval = 1;
  end
end