Stabilization and tracking control of a time-variant linear hyperbolic PIDE using backstepping

Abstract

We extend previous results regarding infinite-dimensional backstepping-based controller design for linear hyperbolic partial (integro-)differential equations (P(I)DEs), and derive a state-feedback controller for a PIDE system with time-varying system parameters. The system state converges to zero in the -norm, in a finite time corresponding to the propagation time between the boundaries. Secondly, the controller is slightly modified to solve an output tracking problem. The derived controllers are demonstrated in simulations. The derived state-feedback controllers can also be combined with state observers into output-feedback controllers.