Decentralized H∞ control for air traffic flow networks modeled by a class of compartmental systems

In this paper, we study the decentralized H
_∞
control problem for air traffic flow (ATF) networks. By dividing the airspace into a number of interconnected regions, we first characterize the traffic flow dynamics by means of a compartmental system approach, and formulate the ATF control problem in a decentralized way, where the controller gain matrix is required to be diagonal and element-restricted. To solve the problem, a novel characterization is presented to ensure that the closed-loop system is asymptotically stable with a prescribed H
_∞
performance. Then, a necessary and sufficient condition for the existence of a required controller is proposed and an iterative linear matrix inequality approach is further developed to solve the design condition. Finally, a simple ATF network is used to show the applicability of the obtained results.