Abstract
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 ofsystems 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 ofa novel inverted pendulum. That is, we prove that it is possible to swing up this pendulum without switching nor measurement of velocities.
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