Finite-time stabilizing dynamic control of uncertain multi-input linear systems

In this paper, a global robust stabilizer is proposed for a class of uncertain linear systems. The stabilizer is a dynamic state feedback controller, which guarantees finite-time convergence to the origin, as well as Lyapunov stability. We first augment the given plant by one additional dynamics and design the stabilizer by combining backstepping and the idea of a dynamic exponent scaling method. Validating the design only on a half-space of the extended state space, the closed-loop system becomes smooth on the space, so that the solution is unique there. In addition, we prove that any solution will reach the origin (by escaping the half-space) in finite time and that the control signals converge to zero by adopting the new concept of degree indicator.