# good books for learning linear matrix inequality with MATLAB examples

3 visualizaciones (últimos 30 días)
Ayesha ayub el 14 de Nov. de 2018
Respondida: Waseem Abbasi el 3 de Jul. de 2019
Hello,
i am in my reasurch phase and badly stuck in LMI coding using matlab. can anyone suggest me some good books on LMI with matlab example please. iam trying to solve the following problem (from "Monitoring of stealthy attack in networked control systems") :
so far i have coded this but it gives me infeasible sol whereas in paper thr range of lambda is [0,0.72]:
clc
close all
clear all
%%%%%%%%%%%%%%%%%%%%%%%%%%SYSTEM DYNAMICS%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
A=[0.6 0 0.34 0.35 ;
0 0.8 0 0.37 ;
0 0 0.5 0 ;
0 0 0 0.9];
B=[1 0 0; 1 0 1; 0 0 2; 0 1 1];
C=[1 0 0 0; 0 1 0 0; 0 0 0 1];
f=[0 0 1 0]';
F=A*f;
H=pinv(C*F);
Ab=A-A*F*H*C;
bta=[ 1 0 1;
2 1 1 ];
sigma=bta*(eye(3)-C*F*H);
% rank(sigma);
cb=sigma*C;
Kb =[0.0057 -0.0028;
-0.0275 0.0618;
0.0041 -0.0178;
0.0077 0.0239];
K =[0.0276 0.0230 0.0229;
0.0252 0.0612 0.0338;
0.0015 -0.0001 -0.0001;
0.0162 0.0235 0.0313 ];
%%
lambda=0;
k=1;
l=zeros(1,91);
n=zeros(1,91);
%%
%LMI PART
for i=1:91
i
setlmis([]);
Y=lmivar(1,[4,1]) ;
%defining first lmi
% |Y sqrt(1-lamda)(YA+KC) sqrt( lamda)(YA_bar+K_bar*C_bar)|
% | sqrt(1-lamda)(YA+KC)' Y 0 | >0
% | sqrt( lamda)(YA_bar+K_bar*C_bar))' 0 Y |
%%
%row 1 (% |Y sqrt(1-lamda)(YA+KC) sqrt( lamda)(YA_bar+K_bar*C_bar)|)
lmiterm([-1 1 1 Y], 1,1); % Y>0
lmiterm([-1 1 2 Y], 1,sqrt(1-lambda)*A); %sqrt(1-lmd)*(YA)
lmiterm([-1 1 2 0], sqrt(1-lambda)*K*C); %sqrt(1-lmd)*(KC)
lmiterm([-1 1 3 Y], 1,sqrt(lambda)*Ab); %sqrt(lmd)*(YA_bar)
lmiterm([-1 1 3 0], sqrt(lambda)*Kb*cb); %sqrt(lmd)*(K_bar C_bar)
%%
%row 2 (|Y 0|)
lmiterm([-1 2 2 Y], 1,1); %Y>0
lmiterm([-1 2 3 0],zeros(4,4)); %4X4 block of zeros
%%
%row 3 (| Y |)
lmiterm([-1 3 3 Y], 1,1); %Y>0
%%
% defining 2nd lmi (Y<I ) (ignoring this LMI is feasible)
lmiterm([2 1 1 Y],1,1); %Y < ...
lmiterm([-2 1 1 0],eye(4)); % ... < I
%%
syslmis=getlmis ;
[tmin,Yfes] = feasp(syslmis);
Y=dec2mat(syslmis,Yfes,Y) ;
Y1(:,:,k)=Y;
K1(:,:,k)=K;
Kb1(:,:,k)=Kb;
L(:,k)=lambda;
%%
a=Y1(:,:,i);
b=Y1(:,:,i)*A+(K1(:,:,i)*C);
c=Y1(:,:,i)*Ab+(Kb1(:,:,i)*cb);
D=[a sqrt(1-L(:,i))*b sqrt(L(:,i))*c;
sqrt(1-L(:,i))*b' a zeros(4,4);
sqrt(L(:,i))*c' zeros(4,4) a];
%%
[R1,p1] = chol(D); %p1=0 implies D>0
[R2,p2] = chol(Y); %p2=0 implies Y>0
[p1,p2]
if(p1==0 && p2==0)
display('__________________________________positive definite____________________________________________')
dummy(:,k)=k ; %for picking lamda from L with index in dummy for wich D>0 & Y>0
lmd(:,k)=lambda;
end
if(p1~=0 || p2~=0)
dummy(:,k)=0;
% lmd(:,k)=-1;s
display('__________________________________not positive definite________________________________________')
end
lambda=lambda+0.01;
k=k+1;
display('_______________________________________________________________________________________________')
end
display(' all lambdas for which Y>0 and D(Y)>0')
lmd
##### 0 comentariosMostrar -2 comentarios más antiguosOcultar -2 comentarios más antiguos

Iniciar sesión para comentar.

### Respuestas (1)

Waseem Abbasi el 3 de Jul. de 2019
I think as far LMI are concerned its better to use Yalimp toolbox as it solve the LMI problem quite effeciently and easily.
##### 0 comentariosMostrar -2 comentarios más antiguosOcultar -2 comentarios más antiguos

Iniciar sesión para comentar.

### Categorías

Más información sobre LMI Solvers en Help Center y File Exchange.

### Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by