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A numerically stable algorithm is derived to compute orthonormal bases for any deflating subspace of a regular pencil hB-A. The method is based on an update of the OZ-algorithm, in order to obtain any desired ordering of eigenvalues in the quasitriangular forms constructed by this algorithm. As applications we discuss a new approach to solve Riccati equations arising in linear system theory. The computation of deflating subspaces with specified spectrum is shown to be of crucial importance here.

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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.

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