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getf(SCI+'/demos/lmitool/lmidem.sci');
// Copyright INRIA
mode(-1);
x_message([' ';
'LMITOOL is a Scilab package for LMI optimization';
' ';
'It can solve the following problem';
' ';
' minimize f(X1,...,XM) ';
'subject to the LME constraints: ';
' Gi(X1,...,XM)=0, i=1,2,...,p,';
'and the LMI constraints: ';
' Hj(X1,...,XM)>=0, j=1,2,...,q.';
' ';
'where';
'X1,...,XM are unknown real matrices';
'f is the objective function, a linear scalar function of the entries of the X''s,';
'Gi''s are affine matrix functions of the entries of the X''s,';
'Hj''s are affine symmetric matrix functions of the entries of the X''s.';
' ';
'For a detailed description and examples consult: ';
' ''LMITOOL: a Package for LMI Optimization in Scilab, User''s Guide'' ';
' ';
' ';
'LMITOOL uses Semidefinite Programming package SP developed by L. Vandenberghe and S. Boyd.']);
while %t
%demo_=x_choose(['H-infinity gain';'Output Feedback';'Sylvester equation'],...
['This is a sample of LMI problems that LMITOOL can solve';
'Select a problem (other examples are given in demos/lmitool directory)']);
select %demo_
case 0
break;
case 1
mode(1)
lmidem(SCI+'/demos/lmitool/normopt.sci');
getf(SCI+'/demos/lmitool/normopt.sci');
x_message(['Let''s try a simple example with 3 states';...
'Edit below A,B,C,D matrices']);
[ok,A,B,C,D]=getvalue('Enter A, B, C, D matrices',['A';'B';'C';'D'],...
list('mat',[3,3],'mat',[3,2],'mat',[2,3],'mat',[2,2]),...
['[0,1,0;2,3,1;-1,-2,0]','[1,0;-2,1;0,1]','[1,2,0;0,1,-2]','[0,0;0,0]']);
if ok then
[X,gopt]=normopt(A,B,C,D);
disp(gopt, 'optimal gama found is:')
disp(gopt-h_norm(syslin('c',A,B,C,D)),...
'check: gopt-h_norm(syslin(''c'',A,B,C,D)=')
end
mode(-1)
case 2
mode(1)
lmidem(SCI+'/demos/lmitool/of.sci');
getf(SCI+'/demos/lmitool/of.sci');
x_message(['Let''s try a simple example with 3 states';...
'Enter A,B,C matrices']);
[ok,A,B,C]=getvalue('Edit below A, B, C matrices',['A';'B';'C'],...
list('mat',[3,3],'mat',[3,2],'mat',[2,3]),...
['[0,1,0;2,3,1;-1,-2,0]','[1,0;-2,1;0,1]','[1,2,0;0,1,-2]']);
if ok then
[P,Q]=of(A,B,C);
disp(P,Q);
end
mode(-1)
case 3
mode(1)
lmidem(SCI+'/demos/lmitool/sylvester.sci');
getf(SCI+'/demos/lmitool/sylvester.sci');
x_message(['Let''s try a simple example with 3 states';...
'Enter A,B,C matrices']);
[ok,A,B,C]=getvalue('Edit below A, B, C matrices',['A';'B';'C'],...
list('mat',[3,3],'mat',[2,2],'mat',[3,2]),...
['[0,1,0;2,3,1;-1,-2,0]','[1,0;-2,1]','[1,2;0,1;1,-2]']);
[X]=sylvester(A,B,C,'c');
disp(X, 'X found is:')
disp(A*X+X*B-C ,'Check: A*X+X*B-C =')
mode(-1)
end
end
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