Nonlinear Feedback Design for Fixed-Time Stabilization of Linear Control 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.