Jean-Michel Coron

Brigitte d'Andréa-Novel, Jean-Michel Coron, Wilfrid Perruquetti

This paper concerns the small-time stabilization of some classes of mechanical systems which are not stabilizable by means of at least continuous state feedback laws. This is the case of nonholonomic mechanical systems, an example being the unicycle robot, or for underactuated mechanical systems, an example being the slider. Explicit time-varying feedback laws leading to small-time stabilization are constructed for these two control systems. The main tools are homogeneity, backstepping, and desingularization technics.

Georges Bastin, Jean-Michel Coron, Amaury Hayat

We study a system of several one-dimensional scalar conservation laws coupled through boundary feedback conditions that combine physical boundary constraints with static feedback control laws. Our first contribution establishes the well-posedness of the system in the space of $L^{\infty}$ entropy solutions. Our second contribution provides a set of sufficient dissipative conditions on the boundary coupling that ensure global exponential stability in the $L^1$ and $L^\infty$ norms.