Global stabilization of multiple integrators with bounded controls

This paper deals with the global stabilization of a chain of integrators by means of bounded feedback. Two nonlinear control laws made of summation of saturation of the state are proposed. The first one extends that of Sussmann, Sontag and Yang [(1994). IEEE Transactions on Automatic Control, 39(12), 2411–2425] and the second proposes variable saturation level to improve the performance. Both remain very simple and significantly improve the efficiency of the approach, which is very competitive with respect to the other existing methods, especially for its performance/complexity ratio. The robustness with respect to measurement delay and model uncertainty is numerically tested.