Stabilization of underactuated mechanical systems via interconnection and damping assignment

The present paper is concerned with the application of the newly developed interconnection and damping assignment (IDA) passivity-based control (PBC) to the problem of stabilization of underactuated mechanical systems. Our main contribution is the characterization of a class of systems for which IDA-PBC yields a smooth stabilizing controller. The class is given in terms of solvability of a partial differential equation. As an illustration we present a dynamic nonlinear output feedback IDA-PBC which "globally" stabilizes (except for a set of initial conditions that has zero measure) the upward position of a novel inverted pendulum. That is, we prove that it is possible to swing up this pendulum without switching nor measurement of velocities. Copyright (C) 2000 IFAC.