KYP lemma for internally positive systems and a tractable class of distributed H-infinity control problems

We consider the KYP lemma for internally positive LTI systems and show that the H
∞
norm of such systems can be evaluated by checking the existence of a certain diagonal quadratic storage function. Once the existence of such a diagonal quadratic storage function is ensured, the problem of finding the optimal H
∞
controller among the class of structured static state feedback controllers attaining internal positivity of the closed loop system becomes convex and tractable.