Application of positive system theory to robust control design

Recently, positive systems have attracted great theoretical interest in many application fields including power systems, chemical systems, transportation systems, system biology, economic and ecological systems. We show that the H-infinity analysis method for positive LTI systems have a distinctive form compared to the standard method for general LTI systems. Namely, the Bounded Real Lemma developed for positive LTI systems suggest that the H-infinity norm of such systems can be evaluated by checking the existence of a certain diagonal quadratic storage function. Due to this attractive property, the problem of finding the optimal H-infinity controller among the class of structured static state feedback controllers attaining internal positivity of the closed loop system becomes convex and tractable. We further propose some new robust control techniques taking special properties of positive systems into account.