L2-gain of Port-Hamiltonian systems and application to a biochemical fermenter model

We consider the Lscr₂-gain of nonlinear Port-Hamiltonian systems. Using the Hamiltonian and an additional scaling matrix, we show that an upper bound on the Lscr₂-gain can be computed by solving a matrix inequality. The Lscr₂-gain is typically used in combination with the small-gain theorem. In particular it can be used to guarantee robust stability with respect to gain-bounded model uncertainties. This application of the Lscr₂-gain is demonstrated with a biochemical fermentation process where the specific cell growth rate is unknown but contained in a parameter interval.