A Lyapunov stability proof for nonlinear-stiffness PD control

A stability proof is presented for a nonlinear PD (NPD) controller and third order systems. Nonlinear-stiffness control has been described previously in the literature and experimentally demonstrated; but to date, no stability proof has been given for systems of degree greater than 2 and the case where the stiff gain exceeds the limit established by the circle criterion. The limitation is important because, for this case, the circle criterion is quite conservative and much of the benefit of NPD control comes with gains greater than could previously be proven to be stable. The stability of 3^rd order systems with nonlinear-stiffness PD control and gains exceeding the circle-criterion limit is established by demonstrating a Lyapunov function. The damping achieved by high-gain NPD control is demonstrated by simulation