On global stabilization of cascaded nonlinear systems

The problem of global smooth stabilization of cascade compositions of nonlinear globally asymptotically stable systems is studied. Global stabilization can be achieved if the first system can be rendered passive for an output that spans the unstable part of the vector field of the second system. This result generalizes earlier stabilizability conditions for the case when the first system is linear. It also provides some insight into the structural properties of the dependence of the second system´s vector field and the first system´s `output´ needed to achieve global stabilization