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

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