Prescribed Performance Regulation in the presence of Unknown Time-Varying Delays

We design a state-feedback controller to impose prescribed performance attributes on the output regulation error for uncertain nonlinear systems, in the presence of unknown time-varying delays appearing both to the state and control input signals, provided that an upper bound on those delays is known. The proposed controller achieves pre-specified minimum convergence rate and maximum steady-state error, and keeps bounded all signals in the closed-loop. We proved that the error is confined strictly within a delayed version of the constructed performance envelope, that depends on the difference between the actual state delay and its corresponding upper bound. Nevertheless, the maximum value of the output regulation error at steady-state remains unaltered, exactly as pre-specified by the constructed performance functions. Furthermore, the controller does not incorporate knowledge regarding the nonlinearities of the controlled system, and is of low-complexity in the sense that no hard calculations (analytic or numerical) are required to produce the control signal. Simulation results validate the theoretical findings.