wxlmi.m

对时间滞后系统进行状态反馈控制器参数设计

clc;
d=1.95
% while tmin<-0.001
% d=1.95

% w0=3.77;
% w1=0.2;
% g=9.81;
% A=[0 1;-w0^2 -2*w1*w0]
% B=[0;-w0./g]
% C=[1 0]
% D=[0];
% sys=ss(A,B,C,D);
% % eig(A)
% sysd=c2d(sys,0.1,'zoh')

a1=[0.9332  0.09064
    -1.288   0.7965];
b1=[-0.001807
    -0.03483];
% eig(A)
i=eye(2);
a2=a1-i;
setlmis([]);
% aa=d2c(sysd,'zoh')%将离散状态方程转化为连续状态方程
p = lmivar(1,[2 1]);
q = lmivar(1,[2 1]);
z = lmivar(2,[2 2]);
y = lmivar(2,[2 2]);
s = lmivar(2,[1 2]);

% 1=newlmi;

lmiterm([1 1 1 p],-1,1);
lmiterm([1 1 1 z],d,1);
lmiterm([1 1 1 y],1,1);
lmiterm([1 1 1 -y],1,1);
lmiterm([1 1 1 q],1,1);

lmiterm([1 2 1 y],-1,1);
lmiterm([1 1 3 p],1,a1');
lmiterm([1 1 4 p],d,a2');
lmiterm([1 2 3 -s],1,b1');
lmiterm([1 2 4 -s],d,b1');

lmiterm([1 2 2 q],-1,1);
lmiterm([1 3 3 p],-1,1);
lmiterm([1 4 4 p],-d,1);

% 2=newlmi;
lmiterm([-2 1 1 z],1,1);
lmiterm([-2 1 2 y],1,1);
lmiterm([-2 2 2 p],1,1);

lmis = getlmis;
[tmin,xfeas] = feasp(lmis);

% end
% disp('tmin====')
% disp(tmin)
% disp(d)
p = dec2mat(lmis,xfeas,p)
q = dec2mat(lmis,xfeas,q)
s = dec2mat(lmis,xfeas,s)
z = dec2mat(lmis,xfeas,z)
y = dec2mat(lmis,xfeas,y)

k=s*inv(p)
%%

% %%
% a1=[-1 2;1 -3]
% a2=[-0.8 1.5;1.3 -2.7]
% a3=[-1.4 0.9;0.7 -2]
% setlmis([]) ;
% p = lmivar(1,[2 1]);
% 
% lmiterm([1 1 1 p],1,a1,'s'); % LMI #1 
% lmiterm([2 1 1 p],1,a2,'s'); % LMI #2 
% lmiterm([3 1 1 p],1,a3,'s'); % LMI #3 
% lmiterm([-4 1 1 p],1,1); % LMI #4: P 
% lmiterm([4 1 1 0],1); % LMI #4: I 
% lmis = getlmis;
% [tmin,xfeas] = feasp(lmis)
% P = dec2mat(lmis,xfeas,p)
%%
% a=[-1 2;2 -3]
% ad=[-0.8 1.5;1.5 -2.7]
% n=10
% b=ones(n,1)
% a=magic(10)
% c=rand(1,10)
% d=10
% 
% setlmis([]) ;
% 
% 
% 
% p=lmivar(1,[10 1]);
% q=lmivar(1,[10 1]);
% v=lmivar(1,[10 1]);
% w=lmivar(2,[10 10]);
% 
% lmiterm([1 1 1 p],1,a+ad,'s'); % LMI #1 
% lmiterm([1 1 1 -w],1,ad); % LMI #1 
% lmiterm([1 1 1 w],ad',1); % LMI #1 
% lmiterm([1 1 1 q],1,1); % LMI #1 
% 
% lmiterm([1 2 1 w],-ad',1); % LMI #1 
% lmiterm([1 3 1 v],1,ad*a); % LMI #1 
% lmiterm([1 3 2 v],1,ad*ad); % LMI #1 
% lmiterm([1 4 1 -w],d,1); % LMI #1 
% lmiterm([1 4 1 p],d,1); % LMI #1 
% 
% 
% lmiterm([1 2 2 q],-1,1); % LMI #1 
% lmiterm([1 3 3 v],-1,1); % LMI #1 
% lmiterm([1 4 4 v],-1,1); % LMI #1 
% 
% lmis = getlmis;
% [tmin,xfeas] = feasp(lmis)
% p = dec2mat(lmis,xfeas,p)
% q = dec2mat(lmis,xfeas,q)
% v = dec2mat(lmis,xfeas,v)
% w = dec2mat(lmis,xfeas,w)
% ad = dec2mat(lmis,xfeas,ad)