tinitial.m

线性时变系统控制器设计的工具包

%  tinitial.m
%
%     usage:   t_init=tinitial(lmi_sys,x_init,lmi_no)
%
%  given an lmi described by lmi_sys:          A(x)<t*B(x)
%  and an initial x:                           x=x_init
%  return the min value of t=t_init that still satisfies the lmi
%  lmi_no is the number of the lmi in lmi_sys
%

% Written by: Lt Paul Blue
%             WL/FIGC-3 Bldg 146
%             2210 Eighth Street Suite 21
%             Wright-Patterson AFB OH 45433-7531
%
%             e-mail: [e-mail]
%             ph: [phone]
%
% Copyright (c) 1996, All Rights Reserved

function t_init=tinitial(lmi_sys,x_init,lmi_no);

if(nargin~=3)
  disp(' usage:   t_init=tinitial(lmi_sys,x_init,lmi_no)');
  return
end

eval=evallmi(lmi_sys,x_init);

[lhs,rhs]=showlmi(eval,lmi_no);

% put in the form B(x)^-1/2*A(x)*B(x)^-1/2<t*I

new_lhs=minv(sqrtm(rhs))*lhs*minv(sqrtm(rhs));

t_init=max(eig(new_lhs));