New Discrete Sliding Mode Control Using Fractional-Order Reaching Law for Nonlinear Systems

This work introduces a novel discrete sliding mode control approach, leveraging a fractional-order reaching law derived from the Grunwald-Letnikov framework. Specifically tailored for discrete Hammerstein nonlinear systems, the proposed reaching law replaces the classical Gao reaching law to address key limitations in robustness and convergence. By integrating fractional calculus principles, this method offers improved adaptability to system uncertainties and external disturbances, ensuring precise and stable control performance. Comprehensive simulation studies are conducted to validate the effectiveness of the proposed approach. The results demonstrate significant performance enhancements, including faster convergence, reduced chattering, and increased robustness, compared to traditional methods. These findings underscore the potential of the proposed fractional-order strategy in advancing control design for complex discrete nonlinear systems.