LMI-Based Nonlinear Control via Implicit Lyapunov Function for Finite-Time Stabilization

This paper deals with finite-time stabilization of uncertain nonlinear SISO systems with relative degree equal to their order. In contrast with former methodologies which were limited to linear systems without uncertainties, this proposal can be applied to a class of nonlinear uncertain systems. The nonlinear control scheme exploits the system nonlinearities and control signal constraints while being able to take into account constant but unknown parametric uncertainties lying in a compact set. The key of such developments is the convex treatment of expressions, which, in addition, allows formulating design conditions as a set of linear matrix inequalities. The solution does not depend on similar works that have been contested in the past. Examples are presented to illustrate the advantages of the proposal over similar recent approaches.