Application of generalised polynomials to the decoupling of linear multivariable systems

Properties of generalised polynomials and generalised polynomial matrices are applied to the problem of the decoupling with Λ-stability of linear square multivariable systems, i.e. decoupling of linear systems with closed-loop poles in a region Λ of the complex plane. We present first some extensions of well known results about generalised polynomials, which are basically defined as rational functions with poles in a symmetric region of the extended complex plane. Then, an application of the concepts to the problem of decoupling with Λ-stability of linear square multivariable systems is presented. The conditions for this problem to have a solution are stated in terms of the row and global zero structure of the system out of the region Λ.