Characterisation of nonlinear and linear time-varying systems by Laplace transformation

In this article we elaborate on various characterisations of nonlinear systems. Specifically, we focus on the frequency-domain characterisation of the class of single-input single-output (SISO) linear time-varying (LTV) systems. We use the model introduced by Wiener using Volterra functional and later elaborated by others. The application of the multidimensional Laplace transform (MDLT) method as a fundamental tool in analysing variable systems and understanding system dynamic behaviours is emphasised. In particular, applications of double or two-dimensional Laplace transform (2DLT) for the analysis and synthesis of LTV circuits and systems are detailed. Examples worked out that illustrate the method and demonstrate its validity in the frequency-domain.