Computing the nearest scattering passive system

In this paper, we consider linear time-invariant control systems that are bounded real (BR), also known as scattering passive. Our main theoretical contribution is to show the equivalence between such systems and port-Hamiltonian (PH) systems whose factors satisfy certain linear matrix inequalities. Based on this result, we propose a formulation for the problem of finding the nearest BR system to a given system and design an algorithm combining alternating optimization and Nesterov's fast gradient method. This formulation also allows us to check whether a given system is BR by solving a semidefinite program and provide a PH parametrization for it. We illustrate our proposed algorithms on real world and synthetic datasets.