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Zbl 1140.93447
Moulay, Emmanuel; Dambrine, Michel; Yeganefar, Nima; Perruquetti, Wilfrid
Finite-time stability and stabilization of time-delay systems. (English)
[J] Syst. Control Lett. 57, No. 7, 561-566 (2008). ISSN 0167-6911

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 2000:: *93D05 Lyapunov and other classical stabilities of control systems
93C15 Control systems governed by ODE
93C10 Nonlinear control systems

Keywords: finite-time stability; finite-time stabilization; time-delay systems

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