A Differential Approach for Obtaining Diagonal Volterra Kernels

A new algorithm is presented for mapping a non-linear auto-regressive with exogenous input model to its Volterra series characteristics in diagonal coordinates. This approach is attractive because it allows functionals to be described as a series of parametrized 1-D convolutions, although it has not been frequently used in system analysis and design, possibly due to the absence of methods for obtaining them from traditional system representations. The proposed algorithm is based on the interpretation that functionals can be viewed as a power series, so that kernels can be isolated using derivatives. The implementation is straightforward and only requires results from multivariate calculus. A simple example and simulation results are presented for supporting the proposed approach, which has the potential for aiding nonlinear systems analysis and synthesis.