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Reduced-order inf. horizon time-inv. discr.-time LQG control for systems with white parameters

Reduced-order inf. horizon time-inv. discr.-time LQG control for systems with white parameters

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08 Jun 2008 (Updated )

Optimal reduced-order compensation of discrete-time linear systems with white parameters

[pm,gm,cm,pms,gms,cms,pva,gva,cva,...
% EX1W :  Data example 1 UKACC Control '98 paper
%         Function specifying a reduced-order infinite horizon
%         discrete-time LQG problem with white paramaters.
%
%         function [pm,gm,cm,pms,gms,cms,pgms,pcms,pva,gva,cva,pgva,pcva,...
%                   v,w,q,r,nc]=ex1w;
%
%         L.G. Van Willigenburg, W.L. De Koning, 13-12-96.
%
  function [pm,gm,cm,pms,gms,cms,pva,gva,cva,...
             v,w,q,r,nc]=ex1w();

% Uncertainty measure beta and compensator order nc
  global beta nc; 
  
% System matrices
  pm = [0.3884    1.6578    0.0613    0.0137         0;
        0.0834    0.6802    0.0948    0.6800         0;
        1.2041    0.9213    0.9395    0.1186         0;
        1.2048    1.4738    1.1904    0.7405         0;
             0         0         0         0    0.9500];
 
  gm = [0.5890    0.0920;
        0.9304    0.6539;
        0.8462    0.4160;
        0.5269    0.7012;
           0         0  ];

  cm = [0.9103    0.2625    0.7361    0.6326    0.9910;
        0.7622    0.0475    0.3282    0.7564    0.3653];

% Model uncertainty computation.
  pk=kron(pm,pm);pva=beta*pk;pms=pk+pva;
  gk=kron(gm,gm);gva=beta*gk;gms=gk+gva;
  ck=kron(cm,cm);cva=beta*ck;cms=ck+cva;
  
% Criterion matrices
  v = diag([0.2470 0.9826 0.7227 0.7534 0.6515]);
  q = diag([0.8847 0.2727 0.4364 0.7665 0.4777]);
  w = diag([0.0727 0.6316]);
  r = diag([0.2378 0.2749]);

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