On simultaneous H∞ control and strong H∞ stabilization

In this note, the simultaneous H∞ control problem is addressed. It is first shown that the existence of a single controller which simultaneously stabilizes two systems with a given H∞ norm level is equivalent to that of a strong H∞ stabilization controller of an associated system. Moreover, the result is extended to the case involving r (>2) systems. Then a sufficient condition for the strong H∞ stabilization is proposed based on the bounded real lemma. Finally, a simple numerical example is presented to show the effectiveness of the result.link_to_subscribed_fulltex