Nested saturation with guaranteed real poles

The global stabilization of asymptotically -controllable linear systems with bounded controls has been studied extensively. An early contribution was by Teel who proposed a set of nested saturators to globally asymptotically stabilize the special case of n-integrators with one input. Using this law however, the closed loop system pole locations depend on the choice of coordinate transformation used to arrive at the control law. In this paper we suggest an approach that allows the designer to pick transformations that facilitate the placement of the closed loop poles on the negative real axis.