Existence and evaluation of almost periodic steady-state responses of mildly nonlinear systems

In this paper, a theorem is given that provides conditions for the existence of, and recursive relations for evaluating, the steady-state response of a certain general type of "mildly nonlinear" time-invariant system with inputs that are asymptotically almost periodic. The response is given in the form of a locally convergent series expansion in which the terms of different order are almost periodic functions. It is shown that the systems considered possess a certain preservation property which implies that, for the large class of inputs addressed by our theorem, the generalized Fourier series for the response actually converges pointwise to the response, and not merely in the usual sense of convergence in the space of almost periodic functions. Although functional expansion techniques play a central role in the proofs, Volterra series methods are not used.