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Preprint 02-2018

Robust port-Hamiltonian representations of passive systems

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Author(s) : Christopher Beattie , Volker Mehrmann , Paul Van Dooren

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 02-2018

MSC 2000

93D09 Robust stability
93C05 Linear systems

Abstract :
We discuss the problem of robust representations of stable and passive transfer functions in particular coordinate systems, and focus in particular on the so-called port-Hamiltonian representations. Such representations are typically far from unique and the degrees of freedom are related to the solution set of the so-called Kalman-Yakubovich-Popov linear matrix inequality (LMI). In this paper we analyze robustness measures for the different possible representations and relate it to quality functions defined in terms of the eigenvalues of the matrix associated with the LMI. In particular, we look at the analytic center of this LMI. From this, we then derive inequalities for the passivity radius of the given model representation.

Keywords : port-Hamiltonian system, positive real system, stability radius, passivity radius, linear matrix inequality

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