Hi. I am trying to solve the iterative lmi algorithm using gevp command in matlab. in part of the algorithm it says:
————————————————————————-
1. A,B,C the state matrices are realized first.
2. Q>0 is selected and a ARE is solved for the unknown P A'P+PA-PBB'P+Q=0
3.Iteration starts i=1 and X(i)=P(obtained from above step); Three unknowns are there: P(i), F, alpha(i)( a scalar)
4.Solve the optimization for P(i),F,alpha(i):
minimize alpha(i) subjected to LMI constraints: 4.1 [ A'P(i)+P(i)A - X(i)BB'P(i) - P(i)BB'X(i) + X(i)BB'X(i) - alpha(i)P(i) (B'P(i)+FC)'; B'P(i)+FC -I ] < 0 4.2 P(i)>0
5. alpha(i) is obtained and checked if alpha(i)<=0
—————————————————————–
so I have written the following code:(Matrix A is 4*4 and Matrix B is 4*1 and Matrix C is 3*4 in my problem)
setlmis([]);P=lmivar(1,[4 1]);F=lmivar(2,[1 3]);lmiterm([1 1 1 0],0)lmiterm([-1 1 1 P],1,1)lmiterm([2 1 1 P],1,A','s')lmiterm([2 1 1 P],-1,(B*B')*X,'s')lmiterm([2 1 1 0],X*(B*B')*X)lmiterm([2 2 1 P],B',1)lmiterm([2 2 1 F],1,C)lmiterm([2 2 2 0],-1)lmiterm([-2 1 1 P],1,1)lmiterm([-2 2 1 0],zeros(1,4))lmiterm([-2 2 2 0],zeros(1,1))lmis = getlmis;[alpha,popt]=gevp(lmis,2)
———————————————————–
but MATLAB says:
* ill-posed problem: the constraint B(x) > 0 might be missing.
Result: could not establish feasibility nor infeasibility
————————————————————————-
What is the problem of my code??? Thanks in advance.
Best Answer