Kernel invariance method for relating continuous-time with discrete-time nonlinear parametric models

A method for defining the equivalence between nonlinear parametric models in continuous-time (differential equations) and discrete-time (difference equations) is presented. The method, termed “kernel invariance method”, is a conceptual extension of the “impulse invariance method” in linear system modeling. It employs the general Volterra model form of nonlinear systems and requires that the sampled continuous-time kernels be identical to the discrete-time kernels. The actual implementation of the method may become unwieldy in the general case, but it appears to be tractable in certain cases of low-order nonlinear systems. An illustrative example of a quadratic system is presented that makes use of 1st order and 2nd-order kernel invariance