Structural Mappings of Bilinear Transformations

Abstract

In this chapter, we present a comprehensive picture of the mapping of structural properties associated with general linear multivariable systems under bilinear and inverse bilinear transformations. We will investigate in depth how the finite and infinite zero structures, as well as the 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. We note that a similar version of this chapter was included earlier in a monograph by the first author i.e., [22], in which he had utilized the results of the bilinear transformations and their structural mapping properties to solve general Riccati equations and discrete-time H _∞ control problems. Nonetheless, this chapter actually builds a bridge for linear system theory between the continuous-time domain and the discrete-time domain. As will be seen shortly in Chapter 8, the results of this chapter will be useful in solving another problem in linear systems, i.e.,system factorizations for discrete-time systems.