How to find the $H_2$ norm of MIMO system in matlab

Question

1. $K$ is given.
2. $A,B_1, B_2, C_1, C_2, D$ are also given.

I want to find the following:

1. $P_{11}, P_{12}, P_{21}, P_{22}$

   

2. And use the resulte in 1., to find the $H_2$ norm of the system:
   

Any hints or example? If we can find 2. directly, it's ok.

The 2. is from the robust control.

Answer 1

If you already have the information then you can simply type

P = ss(A,      [B1,B2],
       [C1;C2],[zeros(size(D12,1),size(D21,2))   D12;
                   D21      zeros(size(D21,1),size(D12,2))];

G = lft(G,K);
n = h2norm(G);

If $G$ is not strictly proper then $H_2$ norm is infinite.