Minimum-phase property of nonlinear systems in terms of a dissipation inequality

A characterization of the minimum-phase property of nonlinear systems in terms of a dissipation inequality is given. It is shown that this characterization contains the minimum-phase property in the sense of Byrnes-Isidori, if the system possesses a well-defined normal form. Furthermore it is shown that, when this dissipation inequalities is satisfied, a kind of minimum-phase behavior follows for general nonlinear systems. Various examples and applications are given which show the usefulness and limits of such a point of view.