Minimal-order realizations for continuous-time 2-power input-output maps

Continuous-time, impulsive time-invariant, 2-power input-output maps are considered. Realizability by a very general class of nonlinear differential systems is characterized simply in terms of the symmetric Volterra transfer function. The characterization leads directly to a family of minimal-order realizations having the (feedforward) structure described by Crouch [6]. Members of the family have states which are related by quadratic homeomorphisms. An especially simple member of the family serves as a canonical form. The development is self-contained and unlike Crouch´s requires only elementary mathematical tools.