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Finite-time stability and stabilization of time-delay systems. (English) Zbl 1140.93447
Summary: 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.
MSC:
93D05Lyapunov and other classical stabilities of control systems
93C15Control systems governed by ODE
93C10Nonlinear control systems