Robust Output Regulation for Uncertain Discrete-Time Linear Systems under the Effect of a Sinusoidal Disturbance

Abstract

This paper studies the robust output regulation problem of uncertain single-input single-output (SISO) discrete-time linear systems. To reject the effect of a sinusoidal disturbance that only the frequency information is known prior, a novel strategy based on adaptive feedforward control (AFC) is developed. Compared with existing regulators for uncertain discrete-time systems, neither the knowledge on the sign of the real part or the imaginary part of the transfer function at the frequency of interest (the so-called strictly positive real (SPR)-like condition), nor persistence of excitation condition is required in this approach. Stability of the closed-loop system is rigorously analyzed using small-gain theorem and Lyapunov-based stability theory. Essentially, the proposed scheme guarantees that all signals of closed-loop system are bounded while the output of system asymptotically converges to zero, which is demonstrated by a numerical example.