Super Twisting Based Lyapunov Redesign for Uncertain Linear Delay Systems

We present a new continuous Lyapunov redesign (LR) methodology for the robust stabilization of a class of uncertain time-delay systems that is based on the so-called super twisting algorithm. The main feature of the proposed approach is that allows one to simultaneously adjust the chattering effect and achieve asymptotic stabilization of the uncertain system, which is lost when continuous approximation of the unit control is considered. At the basis of the super twisting based LR methodology is a well-known class of Lyapunov-Krasovskii functionals. The particular form of the time derivative of this class of functionals allows one to define a delay-free sliding manifold on which some class of smooth uncertainties are compensated.