Robust output regulation problem for linear systems with both input and communication delays

In this paper, we study the robust output regulation problem for linear systems subject to both input time-delay and communication delay via the internal model design approach. Due to the presence of the communication delay, the classical internal model has to be modified so that its dynamics can depend on the delayed state or error-output measurement. A framework for handling the robust output regulation problem for time-delay systems is first established. This framework allows the robust output regulation problem for time-delay systems to be converted into a stabilization problem for an augmented time-delay systems. Using this framework, we have established solvability conditions for the problem by both dynamic state feedback control and dynamic output feedback control subject to the communication delay.