Finite-Time Stability and Stabilization of Polynomial Systems

In this paper we consider the class of polynomial systems and we investigate on their finite-time stability properties. In this analysis, for the first time, finite-time stability is defined with respect to domains with polynomial bounds. A sufficient condition for finite-time stability is obtained, which can be solved recasting the feasibility problem in terms of SDP through SOS programming. Moreover, a nonlinear state-feedback control law is developed to stabilize the system in the finite-time notion. The effectiveness of the stabilizing control law is shown by a numerical example.