IEEE Transactions on Automatic Control, Vol.52, No.11, 2134-2141, 2007
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.