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math.OC2018
Realization of tensor-product and of tensor-Factorization of rational functions
Daniel Alpay, Izchak Lewkowicz
We here first study the state space realization of a tensor-product of a pair of rational functions. At the expense of "inflating" the dimensions, we recover the classical expressi…
math.CV2018
Positive and generalized positive real lemma for slice hyperholomorphic functions
D. Alpay, F. Colombo, I. Lewkowicz +1
In this paper we prove a quaternionic positive real lemma as well as its generalized version, in case the associated kernel has negative squares for slice hyperholomorphic function…
math.CV2018
Composition of rational functions: state-space realization and applications
Daniel Alpay, Izchak Lewkowicz
We define two versions of compositions of matrix-valued rational functions of appropriate sizes and whenever analytic at infinity, offer a set of formulas for the corresponding sta…