Rejection of sinusoids from nonlinearly perturbed uncertain regular linear systems

An application-motivated system class - nonlinearly perturbed regular linear systems (NPRLS) - is considered, and the response of the latter to periodic inputs is characterized. A recently proposed robust control scheme for tracking bandlimited periodic signals by uncertain exponentially stable regular linear systems (RLS) is then applied to an uncertain system belonging to the NPRLS class, whose linearization is an exponentially stable RLS, to reject internally generated sinusoids from the system output. Assuming the uncertain NPRLS to be unknown, but its gain at the frequency of interest known and bounded away from zero, and using the aforementioned characterization, the stability and disturbance rejection of the resulting topology are shown to be guaranteed for sufficiently small nonlinearity.