  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.
