Minimum phase characterization for nonlinear systems with periodic trajectories using differential dissipativity

The minimum phase property is usually defined for the zero dynamics for an equilibrium point, which is asymptotically stable under the zero output constraint. In this paper, it is extended to a more general form of equilibria - periodic trajectories. The zero displacement dynamics is introduced to describe the constrained dynamics with respect to periodic output trajectories. A differential dissipation inequality is derived to characterize the minimum phase property. In this approach, the prior knowledge on neither the periodic trajectories nor the explicit solutions of the zero dynamics is required.