论文H∞ state feedback control for generalized continuous/discrete time-delay system 中第三部分里面的一个例子
系统状态方程：
Matlab程序，LMI工具箱：
clear;
clc;
A=[2 1;0 1];
Ad=[0.2 0.1;0 0.1];
B1=[0.1;0.1];
B2=[1;1];
Bd=[0.1;0.1];
C=[1 1];
Cd=[0.1 0.1];
D11=0.1;
D12=1;
Dd=0.1;
gamma=1;
setlmis([])
% definite the variables
% Q is a symmetric matrix with (2*2)
Q=lmivar(1,[2,1]);
% S1 is a symmetric matrix with (2*2)
S1=lmivar(1,[2,1]);
% S2 is a scalar
S2=lmivar(1,[1,0]);
% M is a vector with (1*2)
M=lmivar(2,[1,2]);
% Confirm every entry in each LMIs
%(1,1)
lmiterm([1,1,1,Q],-1,1)
lmiterm([1,1,1,S2],Bd,Bd')
lmiterm([1,1,1,S1],Ad,Ad')
%(1,2)
lmiterm([1,1,2,Q],A,1)
lmiterm([1,1,2,M],B2,1)
%(1,3)
lmiterm([1,1,3,0],B1)
%(1.4)
lmiterm([1,1,4,S2],Bd,Dd')
lmiterm([1,1,4,S1],Ad,Cd')
%(2,2)
lmiterm([1,2,2,Q],-1,1)
%(2,4)
lmiterm([1,2,4,Q],1,C')
lmiterm([1,2,4,-M],1,D12')
%(2,5)
lmiterm([1,2,5,-M],1,1)
%(2,6)
lmiterm([1,2,6,Q],1,1)
%(3,3)
lmiterm([1,3,3,0],(-gamma^2))
%(3,4)
lmiterm([1,3,4,0],D11')
%(4,4)
lmiterm([1,4,4,0],-1)
lmiterm([1,4,4,S1],Cd,Cd')
lmiterm([1,4,4,S2],Dd,Dd')
%(5,5)
lmiterm([1,5,5,S2],-1,1)
%(6,6)
lmiterm([1,6,6,S1],-1,1)
% Q>0
lmiterm([-2,1,1,Q],1,1)
%S1>0
lmiterm([-3,1,1,S1],1,1)
%S2>0
lmiterm([-4,1,1,S2],1,1)
% definition finish, name is lmis, it can be any name.
lmis=getlmis
[tmin,x]=feasp(lmis)
QQ=dec2mat(lmis,x,Q)
S11=dec2mat(lmis,x,S1)
S22=dec2mat(lmis,x,S2)
MM=dec2mat(lmis,x,M)
程序结果：
tmin =
-0.1027
x =
1.9253
-2.2338
9.1054
16.0928
-14.9665
30.3214
16.0495
-0.2279
-6.2240
QQ =
1.9253 -2.2338
-2.2338 9.1054
S11 =
16.0928 -14.9665
-14.9665 30.3214
S22 =
16.0495
MM =
-0.2279 -6.2240
