Maximizing regions of attraction in backstepping designs for systems with control singularities

For nonlinear systems with control singularities the region of attraction is often only a subset of the region of feasibility (nonsingularity) of the control law. We present conditions under which the backstepping design maximizes the region of attraction by making the regions of feasibility and stability coincide. The key element in the technique is a control Lyapunov function which is singular on the control singularity set and has level sets that always remain in the feasibility region, thus making the feasibility region positively invariant.