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Fixed-time stabilization of linear systems via sliding mode control

The paper presents some new sliding mode control algorithms for uncertain linear plants. The first class of controllers provide global asymptotic stability of the closed-loop system and allow to adjust a guaranteed convergence time of system trajectories into selected neighborhood of the origin independently on domain of initial system states. The design procedure essentially uses block reduction principles and finite-time attractivity properties for polynomial switching surface. The second class of controllers is meant to guarantee global finite-time stability of the closed-loop system with globally bounded settling-time function. The control design algorithms are presented for both single-input and multi-input systems. Theoretical results are supported by numerical simulations.