On Decentralized H-Infinity Optimal Positive Systems

Abstract

This letter gives a closed-form expression for an H-infinity optimal controller with diagonal gain matrix. This phenomenon occurs for certain network systems with acyclic graphs, and potential applications include irrigation networks. Moreover, the above is identified as a special case of a particular controller structure which is shown to be H-infinity optimal if the controller and the resulting closed-loop system are positive. A subsequent result then establishes a connection with open-loop positive systems, and its usefulness in applications is demonstrated on a large set of compartmental systems.