Frequency domain approach to the robust regulator theory for Volterra systems

The robust nonlinear servomechanism problem is studied via the Volterra series in the frequency domain. Based on the knowledge that the steady state response of a Volterra system under the sinusoidal input contains possibly infinitely many frequency components, it is shown that (1) for any specified finitely many frequency components possibly contained in the steady state tracking error, there exists a linear controller that robustly annihilates these components; and (2) robust tracking is possible by a linear controller provided that the Volterra system of the closed loop system is polynomial. These results not only complement the existing results obtained from the state-space domain, but also generates new insights into the problem under consideration.