Design of ‘softer’ robust nonlinear control laws

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