# H infinity norm of error dynamics

Hie all I have two systems as:

sys1 = ss(A1,B1,C1,D);


and a reduced order model as:

sys2 = ss(A2,B2,C2,D);


I want to take the error between them such as:

sys= sys1 - sys2;


I have two questions: 1)- Is this true, that i can write sys as follows?

sys=ss([A1,0;0 A2],[B1;B2],[C1 -C2],0)


2)- When I check the h infinity norm of sys, it is becoming equal to the h infinity norm of sys1 (the high order system) which is very surprising. I am using bounded real lemma to minimize the h infinity norm for this error dynamics using LMI constraints on projection matrices.

Perhaps your reduced order model is not capturing the relevant dynamics of $sys1$? –  copper.hat Jul 23 '12 at 13:53