2019/04/17 by Daniel Bankmann, Bankmann, Daniel, Volker Mehrmann +5
Computer Science · Engineering · Mathematics · #Matrix Theory and Algorithms #Stability and Control of Uncertain Systems #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1904.08202
In this paper formulas are derived for the analytic center of the solution\nset of linear matrix inequalities (LMIs) defining passive transfer functions.\nThe algebraic Riccati equations that are usually associated with such systems\nare related to boundary points of the convex set defined by the solution set of\nthe LMI. It is shown that the analytic center is described by closely related\nmatrix equations, and their properties are analyzed for continuous- and\ndiscrete-time systems. Numerical methods are derived to solve these equations\nvia steepest ascent and Newton-like methods. It is also shown that the analytic\ncenter has nice robustness properties when it is used to represent passive\nsystems. The results are illustrated by numerical examples.\n