Output Feedback Synchronization for Networks of Hyperbolic PDE–ODE Systems

Abstract

This paper considers the output feedback design for the leader-follower synchronization of a network of linear hyperbolic PDE–ODE systems and in particular ODE agents subject to distinct input and output delays. For a communication restricted by a directed graph, a cooperative state feedback is designed using a local backstepping stabilization of the PDE subsystem and a cooperative decoupling transformation. With this, the synchronization problem is traced back to a simultaneous stabilization of the boundary ODEs without introducing additional dynamics in the networked controller. For general PDE–ODE agents an observer using absolute measurements is proposed, while for ODE agents with delays the observer only requires relative measurements. The results of this paper are demonstrated for the output feedback synchronization of ODE agents with distinct input and output delays.