Subzeros of Linear Multivariable Systems

Intuitively, a subzero of a linear multivariable system is a zero of one of its subsystems. In this paper, we give a precise definition of the family of such subzeros by means of the induced exterior map P^(s) associated with a transfer function P(s) : U(s) ¿ Y(s) on one finite-dimensional, rational vector space into another. For such a context, we introduce an exterior model matching problem for subzero design and discuss the algebraic decomposition of the associated controllers. Two explicit decomposition algorithms are outlined; and remarks on the relevance of classical adjoints are included.