State Convergence of Passive Nonlinear Systems With an $L^{2}$ Input

We show that the state of a strictly output passive system with an
L

²
input converges to zero. The result is applied to the disturbance rejection problem (with reference signal zero), where the disturbance can be decomposed into a finite superposition of sine waves of arbitrary but known frequencies and an
L

²
signal. Using an LTI controller, constructed based on the internal model principle, the state trajectories of the plant (and hence also the error signal) converge to zero.