Finite-time and fixed-time stabilization by dual closed-loop controllers

The problem we consider is to find a dual closed-loop controller u(t,p) which will steer the trajectory starting at point x0 to zero in a finite time (and in a fixed time in the second part of the article). We assume that our system is asymptotic stable at the origin, and we give the sufficient conditions for the finite and fixed-time stability. In the second part, we present a new tool for effective finding the dual closed-loop control.