Adaptive global stabilization of uncertain multi-input linear time-delay systems by PDE full-state feedback

A majority of recently published results about control of systems with multi-input time-delay ask for a perfect knowledge of the system itself. To overcome this disadvantage, this paper investigates adaptive control methodology of multi-input linear time-invariant (LTI) systems under a coexistence of classic types of uncertainties, such as unknown and distinct multi-actuator delays, unknown parameters and unmeasurable state in the ordinary differential equation (ODE) part. Making use of the idea of a transport partial differential equation (PDE) representation of the delayed input, a unity-rescaled backstepping transformation and predictor-based PDE full-state feedback is developed to achieve global stabilization for uncertain LTI systems with multi-input time-delay.