On the use of control Lyapunov R-functions for nonlinear stabilization

Control Lyapunov functions provide a fundamental tool to support control design when robustness, constraints fulfillment and optimality have to be simultaneous addressed in system stabilization. However, such general control problem is very challenging and almost impossible to be solved using a single control Lyapunov function. The recent framework of R-functions allow the design of innovative control Lyapunov functions having smooth and non-homothetic level sets. In particular, given a control Lyapunov function with a "large" domain of attraction and a second one guaranteeing local optimality, our merging procedure yields the controlled domain of attraction of the former and the local performance of the latter.