Analysis and synthesis of a class of nonlinear systems

A unified approach for the analysis and synthesis of a class of nonlinear systems is discussed. The analytical approach is based on the Volterra series representation of the input/output relationship of nonlinear systems. A canonic structure is presented for a class of nonlinear systems. The necessary and sufficient condition for the realizability of a given nonlinear system in terms of the canonic structure is presented. This synthesis procedure is based on a simple algorithm for separating a multivariable polynomial using the zeroes of a single variable polynomial. The synthesis procedure is also shown to yield computationally simpler models for a class of nonlinear systems.