Quantitatively Hyper-Positive Real Functions
Optimization and Control
2019-12-19 v1 Functional Analysis
Abstract
Hyper-Positive real, matrix-valued, rational functions are associated with absolute stability (the Lurie problem). Here, quantitative subsets of Hyper-positive functions, related through nested inclusions, are introduced. Structurally, this family of functions turns out to be matrix-convex and closed under inversion. A state-space characterization of these functions, through a corresponding Kalman-Yakubovich-Popov Lemma is given. Technically, the classical Linear Matrix Inclusions, associated with passive systems, are here substituted by Quadratic Matrix Inclusions.
Cite
@article{arxiv.1912.08248,
title = {Quantitatively Hyper-Positive Real Functions},
author = {Daniel Alpay and Izchak Lewkowicz},
journal= {arXiv preprint arXiv:1912.08248},
year = {2019}
}