PASSIVITY PROPERTIES FOR STABILIZATION OF CASCADED NONLINEAR-SYSTEMS

We study the problem of global smooth stabilization of cascade compositions of nonlinear globally asymptotically stable systems. Our main result is that global stabilization can be achieved if we can render the first system strictly passive for an output which 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. Also, it provides some insight on the ("energy dissipation") properties of the dependence of the second system vector field and the first systems "output" needed to achieved global stabilization.