@unpublished{BankmannMehrmannNesterovetal., author = {Bankmann, Daniel and Mehrmann, Volker and Nesterov, Yurii and Van Dooren, Paul}, title = {Computation of the analytic center of the solution set of the linear matrix inequality arising in continuous- and discrete-time passivity analysis}, 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 The results are illustrated by numerical examples.}, language = {en} } @unpublished{MehrmannVanDooren, author = {Mehrmann, Volker and Van Dooren, Paul}, title = {Optimal robustness of port-Hamiltonian systems}, abstract = {We construct optimally robust port-Hamiltonian realizations of a given rational transfer function that represents a passive system. We show that the realization with a maximal passivity radius is a normalized port-Hamiltonian one. Its computation is linked to a particular solution of a linear matrix inequality that defines passivity of the transfer function, and we provide an algorithm to construct this optimal solution. We also consider the problem of finding the nearest passive system to a given non-passive one and provide a simple but suboptimal solution.}, language = {en} }