Preprint 7-2019

Optimal robustness of port-Hamiltonian systems

Author(s) : Volker Mehrmann , Paul Van Dooren

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 7-2019

MSC 2000

93D09 Robust stability

93C05 Linear systems

Abstract :
We construct optimally robust port-Hamiltonian realizations of a given rational transfer function that represents a passive system. We show that the realization with a maximal passivity radius is a normalized port-Hamiltonian one. Its computation is linked to a particular solution of a linear matrix inequality that defines passivity of the transfer function, and we provide an algorithm to construct this optimal solution. We also consider the problem of finding the nearest passive system to a given non-passive one and provide a simple but suboptimal solution.

Keywords : Linear matrix inequality, port-Hamiltonian system, passivity, robustness