A method for constructing minimal linear-analytic realizations for polynomial systems

For a polynomial nonlinear system described in terms of regular transfer functions, the shift-realization approach to constructing minimal bilinear realizations is modified to yield a method for constructing minimal linear-analytic realizations. For brievity, the case of degree-2 polynomial systems is considered. The degree-3 case can be treated in a similar, explicit fashion, but the notation used here becomes too cumbersome for systems of degree ?? 4.