Finite order representations of infinite dimensional bilinear models of nonlinear systems

We show that QLS (quadratic linear systems) yield an exact representation of nonlinear, quadratic integrable input affine system as bilinear models do. However, the QLS representation is shown to be finite dimensional in most cases, while the bilinear system usually requires an infinite dimension. The dimension of the bilinear model is never lower than the dimension of the QLS model. This paper gives sufficient conditions for a finite dimensional representation.