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

Andrey Polyakov (1)

1 NON-A - Non-Asymptotic estimation for online systems

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.

Domaines: Automatique

Andrey Polyakov. Nonlinear feedback design for fixed-time stabilization of Linear Control Systems. IEEE Transactions on Automatic Control, 2011, 57 (8), pp.2106-2110. ⟨10.1109/TAC.2011.2179869⟩. ⟨hal-00757561⟩