State-space approach to the bilinear transformation and some extensions

The author presents a method to perform bilinear transformation on the variable in a polynomial or a rational function. The method uses state-space representation and is based on identifying the transformations in state-space framework that correspond to the bilinear transformation. Also, a similar procedure is developed for the inverse transformation, sometimes known as the w-transformation. Some special cases of the bilinear transformation are also discussed. Examples are used to illustrate the method presented here. Combined with powerful software available for matrix computations, these methods should provide a fast way of performing the transformations discussed here