A Unified Framework for Continuous/Discrete Positive/Bounded Real State-Space Systems
Optimization and Control
2021-02-03 v3 Operator Algebras
Abstract
There are four variants of passive, linear time-invariant systems, described by rational functions: Continuous or Discrete time, Positive or Bounded real. By introducing a quadratic matrix inequality formulation, we present a unifying framework for state-space characterization (a.k.a. Kalman-Yakubovich-Popov Lemma) of the above four classes of passive systems. These four families are matrix-convex as rational functions, and a slightly weaker version holds for the corresponding balanced, state-space realization arrays.
Cite
@article{arxiv.2008.04635,
title = {A Unified Framework for Continuous/Discrete Positive/Bounded Real State-Space Systems},
author = {I. Lewkowicz},
journal= {arXiv preprint arXiv:2008.04635},
year = {2021}
}