# Cvx - infeasible

Hi
I have a problem as bellow but i don’t know which term makes it infeasible .
thank you
clc
clear all
close all
%% unstable plant of order n = 3
A = [1.2 2.4 -1.5;.9 0 -1;1.3 2.6 -.8];

% A = [.2 .4 -.5;.9 0 -1;.3 .6 -.8];

Ad = [1.9 .5 1.3;-.1 .1 0;.2 1.1 -1.1];
B = [1.2;0;-2];
C = [3 -1 2];
%controability & detecability
Co = ctrb(A,B);
unco = length(A) - rank(Co);
Ob = obsv(A,C);
unob = length(A)-rank(Ob);

% parameter
mu = .8 ;
delta = .4;
d2 = 4;d1 = 2;dbar = d2-d1+1;
n = size(A,1);
[n,m] = size(B);
%uncertainty part of plant
M1 =[.1;0;.2];
M2 =.2;
N1 =[1 -1 1];
N2 =[1 0 2];
N3 =.1;
epsilon = .5
%% convex of design controller

cvx_begin sdp
% cvx_solver sedumi

variable X(n,n) nonnegative symmetric
variable Y(n,n) nonnegative symmetric
variable Q(2n,2n) nonnegative
variable QI(2n,2n) nonnegative

variable w(n,n) nonnegative
variable E(m,m) nonnegative

variable AT(n,n) ;
variable BT(n,m) ;
variable CT(q,n) ;
variable DT(q,m) ;

variable gama1 nonnegative;
variable gama2 nonnegative;

Q1 = Q(1:3,1:3);
Q2 = Q(1:3,4:6);
Q3 = Q(4:6,4:6);

QI1 = QI(1:3,1:3);
QI2 = QI(1:3,4:6);
QI3 = QI(4:6,1:3);
QI4 = QI(4:6,4:6);

omega1 = YA’+muCT’*B’;
omega2 = A’X+C’BT’;
omega3 = Y
N1’+mu
CT’*N3’;

minimize gama1*delta +(inv(mu)-1)*gama2

subject to
% % H_infinte lmi conditiohn
[-Y -eye(n) zeros(n) zeros(n) zeros(n,m) omega1 AT zeros(n,m) zeros(n,m) omega3 YN1’ CT’ Y w;
-eye(n) -X zeros(n) zeros(n) zeros(n,m) A’ omega2 zeros(n,m) zeros(n,m) N1’ N1’ zeros(n,m) eye(n) zeros(n);
zeros(n) zeros(n) -Q1 -Q2 zeros(n,m) Ad’ Ad’X zeros(n,m) zeros(n,m) N2’ zeros(n,m) zeros(n,m) zeros(n) zeros(n);
zeros(n) zeros(n) -Q2’ -Q3 zeros(n,m) zeros(n) zeros(n) zeros(n,m) zeros(n,m) zeros(n,m) zeros(n,m) zeros(n,m) zeros(n) zeros(n);
zeros(m,n) zeros(m,n) zeros(m,n) zeros(m,n) -gama1
eye(m) mu
B’ muB’X zeros(m) zeros(m) muN3’ zeros(m) eye(m) zeros(m,n) zeros(m,n);
B -Y -eye(n) M1 zeros(n,m) zeros(n,m) zeros(n,m) zeros(n,m) zeros(n) zeros(n);
AT’ omega2’ XAd zeros(n) muXB -eye(n) -X XM1 BT*M2 zeros(n,m) zeros(n,m) zeros(n,m) zeros(n) zeros(n);
zeros(m,n) zeros(m,n) zeros(m,n) zeros(m,n) zeros(m) M1’ M1’X -inv(epsilon)eye(m) zeros(m) zeros(m) zeros(m) zeros(m) zeros(m,n) zeros(m,n);
zeros(m,n) zeros(m,n) zeros(m,n) zeros(m,n) zeros(m) zeros(m,n) M2’BT’ zeros(m) -inv(epsilon)eye(m) zeros(m) zeros(m) zeros(m) zeros(m,n) zeros(m,n);
omega3’ N1 N2 zeros(m,n) mu
N3 zeros(m,n) zeros(m,n) zeros(m) zeros(m) -epsilon
eye(m) zeros(m) zeros(m) zeros(m,n) zeros(m,n);
(N1
Y) N1 zeros(m,n) zeros(m,n) zeros(m) zeros(m,n) zeros(m,n) zeros(m) zeros(m) zeros(m) -epsilon
eye(m) zeros(m) zeros(m,n) zeros(m,n);
CT zeros(m,n) zeros(m,n) zeros(m,n) eye(m) zeros(m,n) zeros(m,n) zeros(m) zeros(m) zeros(m) zeros(m) -eye(m) zeros(m,n) zeros(m,n);
Y eye(n) zeros(n) zeros(n) zeros(n,m) zeros(n) zeros(n) zeros(n,m) zeros(n,m) zeros(n,m) zeros(n,m) zeros(n,m) -inv(dbar)*QI1 -inv(dbar)*QI2;
w’ zeros(n) zeros(n) zeros(n) zeros(n,m) zeros(n) zeros(n) zeros(n,m) zeros(n,m) zeros(n,m) zeros(n,m) zeros(n,m) -inv(dbar)*QI3 -inv(dbar)*QI4]<=0

cvx_end

S = (eye(n) - X*Y)*inv(w’)

Cc = CTinv(w)’
Bc = inv(S)BT
Ac = (inv(w)
(AT-Y
A’X-muw*Cc’*B’X-YC’*Bc’*S’)*inv(S’))’
sys = ss(Ac,Bc,Cc,0,0.1)
K =tf(sys)
pzmap(sys)

Your problem is not reproducible for me because it uses toolbox functions I don’t have.

Other than nonnegativity (and symmetry) constraints, your problem has only a single LMI constraint. You could check whether at least all the diagonal blocks in the LMI are satisfied individually (which are necessary but not sufficient for the LMI to be feasible). If they are not all feasible, then focus on why. Anyhow, I gave you more detailed advice some months back on diagnosing infeasibility in previous threads on pretty much the same problem. You can also read https://yalmip.github.io/debugginginfeasible/ .