direkt zum Inhalt springen

direkt zum Hauptnavigationsmenü

Sie sind hier

TU Berlin

Inhalt des Dokuments

Preprint 6-2019

Computation of the analytic center of the solution set of the linear matrix inequality arising in continuous- and discrete-time passivity analysis

Source file is available as :   Portable Document Format (PDF)

Author(s) : Daniel Bankmann , Volker Mehrmann , Yurii Nesterov , Paul Van Dooren

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 6-2019

MSC 2000

93D09 Robust stability
49M15 Methods of Newton-Raphson, Galerkin and Ritz types

Abstract :
In this paper formulas are derived for the analytic center of the solution set of linear matrix inequalities (LMIs) defining passive transfer functions. The algebraic Riccati equations that are usually associated with such systems are related to boundary points of the convex set defined by the solution set of the LMI. It is shown that the analytic center is described by closely related matrix equations, and their properties are analyzed for continuous- and discrete-time systems. Numerical methods are derived to solve these equations via steepest ascent and Newton-like methods. It is also shown that the analytic center has nice robustness properties when it is used to represent passive systems. The results are illustrated by numerical examples.

Keywords : Linear matrix inequality, analytic center, passivity, robustness

Notes :
Supplementary code: https://doi.org/10.5281/zenodo.2643171

Zusatzinformationen / Extras


Schnellnavigation zur Seite über Nummerneingabe