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Main Title: Computation of the analytic center of the solution set of the linear matrix inequality arising in continuous- and discrete-time passivity analysis
Author(s): Bankmann, Daniel
Mehrmann, Volker
Nesterov, Yurii
Van Dooren, Paul
Type: Article
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 descent and Newton 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.
Subject(s): algebraic Riccati equation
analytic center
linear matrix inequality
positive real system
Issue Date: 23-Jul-2020
Date Available: 4-Mar-2021
Language Code: en
DDC Class: 510 Mathematik
Sponsor/Funder: TU Berlin, Open-Access-Mittel – 2020
DFG, 361092219, Verteilte dynamische Netzsicherheitssteuerung in Elektroenergiesystemen der nächsten Generation
DFG, 239904186, TRR 154: Mathematische Modellierung, Simulation und Optimierung am Beispiel von Gasnetzwerken
Journal Title: Vietnam Journal of Mathematics
Publisher: SpringerNature
Volume: 48
Issue: 4
Publisher DOI: 10.1007/s10013-020-00427-x
Page Start: 633
Page End: 659
EISSN: 2305-2228
ISSN: 2305-221X
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik » FG Numerische Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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