Compute H-infinity norm in Matlab

Question

Please can someone write a command in Matlab for calculating $H_{\infty}$ norm for the following system:

$$\frac{d}{dt}z(t)=Az(t)+Bu(t)+Fw(t)$$ $$y(t)=Cz(t)+Du(t)$$

where $A$, $B$, $C$, $D$, and $F$ are real valued 2×2 matrices.

I have tried the following code, but it does not work:

A = [0 2; 8 1]
B = [1 0; 2 1]
F = [-1 2; -4 3]
C = [2 0; 0 1] 
D = [1 0; 0 0]
sys = ss(A,B,F,C,D); 

norm(sys,inf)

Answer 1

The $\mathcal{H}^{\infty}$ norm is specified from one vector input to one vector output. Right now, you have written things with two inputs. So you need to reorganize your $A,B,C,D$ matrices.