H∞H∞ model reduction for port-controlled Hamiltonian systems

This paper is concerned with the problem of H∞H∞ model reduction for the linear port-controlled Hamiltonian systems. The development includes both the continuous- and discrete-time cases. Some sufficient conditions are obtained for the existence of solutions in terms of linear matrix inequalities (LMIs) and a coupling non-convex rank constraint set. In addition, an explicit parametrization of the desired reduced-order model can be constructed if these conditions are satisfied. Furthermore, the conditions based on the strict LMIs without rank constraint are derived for the zeroth-order H∞H∞ approximation problem. Finally, the effectiveness of the proposed model reduction method is illustrated via a practical example.