A polynomial approach to the realization of J-lossless behaviors

Abstract

We consider the problem of realizing lossless behaviours with respect to the supply rate equal to the scalar product of the input and of the derivative of the output variables. Using polynomial algebraic method we devise a realization procedure which, starting from an image representation, yields the same state representation used by van der Schaft and Oeloff in the context of model reduction. We also apply the insights derived from this realization procedure to the synthesis of lossless mechanical systems with given transfer functions using springs and masses