Spectral analysis of block structured nonlinear systems

It is a challenge to investigate if frequency domain methods can be used for the analysis or even synthesis of nonlinear dynamical systems. However, the effects of nonlinearities in the frequency domain are non-trivial. In this paper analytical tools and results to analyze nonlinear systems in the frequency domain are presented. First, an analytical relationship between the parameters defining the nonlinearity, the LTI dynamics and the output spectrum is derived. These results allow analytic derivation of the corresponding higher order sinusoidal input describing functions (HOSIDF). This in turn allows to develop novel identification algorithms for the HOSIDFs using identification experiments that apply broadband excitation signals, which significantly reduces the experimental burden previously associated with obtaining the HOSIDFs. Finally, two numerical examples are presented. These examples illustrate the use and efficiency of the theoretical results in the analysis of the effects of nonlinearities in the frequency domain and broadband identification of the HOSIDFs.