An algorithm for feedback stabilization with respect to saturating controls using universal formulas for control-Lyapunov functions

Smooth control-Lyapunov functions (CLFs) have been used extensively in modern feedback control design. CLF´s were used to give explicit universal formulas for feedback stabilization. These formulas give feedback which render systems globally asymptotically stable with respect to the origin and which are `almost smooth´ for systems with smooth vector fields. The feedbacks are also real analytic on Rⁿ (0) for cases where the known CLF is real analytic and the system has real analytic vector fields. By a universal formula, one can define an expression for a stabilizing feedback law in terms of the directional derivatives of the given CLF in the directions of the vector fields that define the system. The exact definitions of universal formulas and CLF´s are given. This paper extends the results of Malisoff et al. (1999) by giving universal formulas for control systems on Rⁿ