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

Abstract

We design a state-feedback controller to impose prescribed performance attributes on the output stabilization 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. Nevertheless, the maximum value of the output 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.