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
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