How to define complex LMI with different type of variables

Dear community:

This is my first post and I am a relatively new user of the robust control toolbox. I am trying to solve a LMI system in which I try to replicate the results from an article (https://people.kth.se/~kallej/papers/networked_control_ifac14liu.pdf). In this paper a LMI term is defined based on different matrix variables that are on themself defined over other matrix variables which are again defined from an equation with matrix variables. As this is hard to explain with words this is the problem with matrix symbols

My principal inequality term is

which I describe with the code (the 3N is because there are other terms described before)

 lmiterm([3*N 1 1 sigma11],1,1); %
 lmiterm([3*N 1 2 sigma12'],1,1);%
 lmiterm([3*N 2 2 sigma22],1,1);

Then the variables of that lmiterm are defined as

where , , P , , , of size [n_state n_state] and all the and of size [n_i n_i] are the lmi basic variables (all the other terms are constant and given), which I think I define correctly with

 P=lmivar(2,[n_state,n_state]);
    Q=lmivar(2,[n_state,n_state]);
    S0=lmivar(2,[n_state,n_state]);
    S1=lmivar(2,[n_state,n_state]);
    R0=lmivar(2,[n_state,n_state]);
    [R1,n,sR1]=lmivar(2,[n_state,n_state]);
    [S12,n,sS12]=lmivar(2,[n_state,n_state]);
    Ql=cell(1,N);
    U=cell(1,N);
    for i=1:N
        Ql{i}=lmivar(2,[n_outputs(i),n_outputs(i)]);
        U{i}=lmivar(2,[n_outputs(i),n_outputs(i)]);
    end
    lmiterm([-1 1 1 P],1,1); %P>0
    lmiterm([-2 1 1 Q],1,1); %Q>0
    lmiterm([-3 1 1 S0],1,1); %S0>0
    lmiterm([-4 1 1 S1],1,1); %S1>0
    lmiterm([-5 1 1 R0],1,1); %R0>0
    lmiterm([-6 1 1 R1],1,1); %R1>0
    lmiterm([-7 1 1 S12],1,1); %S12>0
    for i=1:N
      lmiterm([-(i+7) 1 1 Q{i}],1,1); %Q>0
      lmiterm([-(i+N+7) 1 1 U{i}],1,1); %U>0  
    end

My problem is that i do not know how to describe in code any of the  , φ and H. From the documentation I know I can define complex structures like and with lmivar of type 3. I try to describe them with it but I do not know how to ensure the symetry given by the * in and to describe the individual matrix multiplication of each term from . Also, I do not know how to write φ, and H, as they are equations containing a mixture of operations with constant terms and LMI variables which then needs to be inside a matrix equation which then is inserted into a term. Also I do not know how to describe the diag function of with the variables and constant terms in a lmi var that uses the basic variables in the equations along the constant terms. I suppose almost all of this is also achievable defining LMI variables of type 3 but I could not find documentations or examples that could guide me. I would really appreciate your help if anyone could tell me how to properly describe that problem.