force sdpvar matrix to create a matrix with zero element

[Mahyar Madani]

Dear Johan

I designed RMPC Controller with LMI technique and i have 3 sdpvar in question(that is Y(2x20),Q(20x20),gama) so i have many Constraints which one of them is

constraints1=[Q,Q*A'+Y'*B',(Q*Q1^0.5)',Y'*R1.^0.5;(Q*A'+Y'*B')',Q,0,0;Q*Q1^0.5,0,gama,0;Y*R1.^0.5,0,0,gama]

and F=Y*Q^-1

my problem is: How can i force the many elements of matrix F(2x20) to be zero value?

these value of F must be zero: 10,12,13,15,18,20,21,23,26,28,29,31,34,36,37,39

Best Regards
Mahyar Madani

[Johan Löfberg]

Not possible.

Structural constraints on state-feedback gains is very hard. Trivial to formulate in original nonconvex form of the problem, and impossible to impose on the convexified reformulation (and if you sort out a formulation of it in the reformulated form, it would lead to nonconvexity, and you would be back at where you started)