Hi,
I think there was some errors in your lmiterm, i prefer to use the gui editor "lmiedit" it helps to avoid errors, with using it i can produce the same results that you have in the book.
%Definition of the Matrices
% Clear the workspace
clc
clear all
% Specify parameter matrices
A = [-1 0 1;
0 2 -1;
2 0 -3]
Ad = [ 1 0 1;
2 1 1;
0 0 -1]
B = [1 1;
1 2;
0 1]
d = 0.1;
% LMI problem definition
%% Definition of the Decision Variables
setlmis([]);
X = lmivar(1,[3 1]);
W = lmivar(2,[2,3]);
Beta = lmivar(1,[1 1]);
% Definitions of the LMI
% LMI #1
% LMI #1 LMI(1,1)
lmiterm([1 1 1 X],1,A','s'); % LMI #1: X*A'+A*X
lmiterm([1 1 1 X],1,Ad','s'); % LMI #1: X*Ad'+Ad*X
lmiterm([1 1 1 W],B,1,'s'); % LMI #1: B*W+W'*B'
lmiterm([1 1 1 0],d*Ad*Ad'); % LMI #1: d*Ad*Ad'
lmiterm([1 2 1 X],d*A,1); % LMI #1: d*A*X
lmiterm([1 2 1 W],d*B,1); % LMI #1: d*B*W
lmiterm([1 2 2 Beta],.5*d,-eye(3),'s'); % LMI #1: -d*Beta*eye(3) (NON SYMMETRIC?)
lmiterm([1 3 1 X],d*Ad,1); % LMI #1: d*Ad*X
lmiterm([1 3 3 Beta],.5*d,eye(3),'s'); % LMI #1: d*Beta*eye(3) (NON SYMMETRIC?)
lmiterm([1 3 3 0],-d*eye(3)); % LMI #1: -d*eye(3)
lmiterm([-2 1 1 X],1,1); % LMI #2: X
lmiterm([-3 1 1 Beta],1,1); % LMI #3: Beta
lmiterm([4 1 1 Beta],1,1); % LMI #4: Beta
lmiterm([-4 1 1 0],1); % LMI #4: 1
stabilz2=getlmis;
%LMI Solution
[tmin,xfeas] = feasp(stabilz2);
Xvalue = dec2mat(stabilz2,xfeas,X)
Wvalue = dec2mat(stabilz2,xfeas,W)
Betavalue = dec2mat(stabilz2,xfeas,Beta)
k = Wvalue*inv(Xvalue)
