Structural Mappings of Bilinear Transformations

Abstract

We recall in this chapter the work of Chen and Weller [40] on bilinear and inverse bilinear transformations of linear time-invariant systems. Their result presents a comprehensive picture of the mapping of structural properties associated with general linear multivariable systems under bilinear and inverse bilinear transformations. They have completely investigated the problem of how the finite and infinite zero structures, as well as invertibility structures of a general continuous-time (discrete-time) linear time-invariant multivariable system are mapped to those of its discrete-time (continuous-time) counterpart under the bilinear (inverse bilinear) transformation. It is worth noting that we have added in this chapter some new results on the mapping of geometric subspaces under the bilinear (inverse bilinear) transformation.