We show that the Lyapunov function used in backstepping feedback desig
ns for uncertain nonlinear systems leads to unnecessarily 'hard' contr
ol laws having undesirable high-gain properties. We present a new Lyap
unov function and use it to design 'softer' control laws which exhibit
the high-gain properties to a much lesser extent. We show that the 's
oft' designs eliminate the chattering exhibited by the 'hard' designs
and achieve the same or better performance with less control effort.