Finite-time stability and stabilization of time-delay systems

Finite-time stability and stabilization of retarded-type functional differential equations are developed. First, a theoretical result on finite-time stability inspired by the theory of differential equations, using Lyapunov functionals, is given. As it may appear not easily usable in practice, we show how to obtain finite-time stabilization of linear systems with delays in the input by using an extension of Artstein’s model reduction to nonlinear feedback. With this approach, we give an explicit finite-time controller for scalar linear systems and for the chain of integrators with delays in the input.