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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…