A new convergence analysis for the Volterra series representation of nonlinear systems

The convergence of the Volterra series representation of nonlinear systems is the fundamental requirement for the analysis of nonlinear systems in the frequency domain. In the present study, a new criterion is derived to determine the convergence of the Volterra series representation of nonlinear systems described by a NARX (Nonlinear Auto Regressive with eXegenous input) model. The analysis is performed based on a new function known as Generalized Output Bound Characteristic Function (GOBCF), which is defined in terms of the input, output and parameters of the NARX model of nonlinear systems. Compared to the existing results, the new criterion provides a much more rigorous and effective approach to the analysis of the convergence conditions and properties of the Volterra series representation of nonlinear systems. Two case studies have been used to demonstrate the effectiveness of the new convergence analysis criterion and the advantages of the new analysis over those produced by existing approaches.