Nonlinear feedback design for fixed-time stabilization of Linear Control Systems

Andrey Polyakov 1
1 NON-A - Non-Asymptotic estimation for online systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : Nonlinear control algorithms of two types are presented for uncertain linear plants. Controllers of the first type are stabilizing polynomial feedbacks that allow to adjust a guaranteed convergence time of system trajectories into selected neighborhood of the origin independently on initial conditions. The control design procedure uses block control principles and finite-time attractivity properties of polynomial feedbacks. Controllers of the second type are modifications of the second order sliding mode control algorithms. They provide global finite-time stability of the closed-loop system and allow to adjust a guaranteed settling time independently on initial conditions. Control algorithms are presented for both single-input and multi-input systems. Theoretical results are supported by numerical simulations.
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Andrey Polyakov. Nonlinear feedback design for fixed-time stabilization of Linear Control Systems. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2012, 57 (8), pp.2106-2110. ⟨hal-00757561⟩

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