Discrete sliding mode control based on a new fractional order power reaching law

This paper presents a robust controller design for a discrete linear system, dealing with internal and external disturbances. The main focus is to reduce chattering, minimize undesirable oscillations, and enhance robustness against disturbances using a new discrete sliding mode control. The novel approach involves replacing the classical Gao’s reaching law with a fractional order reaching law based on the Grunwald–Letnikov definition, leading to advantages like a simplified algorithm and improved performance against disturbances. The performances of the suggested method are evaluated through two simulation examples.