On the Finite-Time Stabilization of Uncertain Nonlinear Systems With Relative Degree Three

This technical note discusses a finite-time stabilization problem in a nonlinear, uncertain, environment. The main result of the present note is presented making reference to a triple integrator affected by bounded uncertainties and subject to “hard” measurement nonlinearities such that the sign of the state variables is the only reliable information available for feedback. We propose a discontinuous control scheme guaranteeing the practical finite-time annihilation of the three state variables. Constructive proof and computer simulations, as well as guidelines for practical implementations, are provided throughout this technical note.