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];
eig(blkdiag(A,Ad))
%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);
[q,n] = size©;
%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 = YN1’+muCT’*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) -gama1eye(m) muB’ muB’X zeros(m) zeros(m) muN3’ zeros(m) eye(m) zeros(m,n) zeros(m,n);
omega1’ A Ad zeros(n) muB -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) muN3 zeros(m,n) zeros(m,n) zeros(m) zeros(m) -epsiloneye(m) zeros(m) zeros(m) zeros(m,n) zeros(m,n);
(N1Y) N1 zeros(m,n) zeros(m,n) zeros(m) zeros(m,n) zeros(m,n) zeros(m) zeros(m) zeros(m) -epsiloneye(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-YA’X-muw*Cc’*B’X-YC’*Bc’*S’)*inv(S’))’
sys = ss(Ac,Bc,Cc,0,0.1)
K =tf(sys)
pzmap(sys)