H∞ Sliding Mode Control: A Recent Review of Applications and Design Methods

The $H_{\infty }$ Sliding Mode Control ( $H_{\infty }$ SMC) approach was introduced at the onset of this millennium as a proficient strategy integrating sliding mode and $H_{\infty }$ control principles to leverage their robust attributes while avoiding inherent limitations, thereby facilitating the control of complex perturbed nonlinear systems. This review study explores noteworthy advances in the academic community of $H_{\infty }$ SMC from January 2019 to September 2024, revealing notable progress with cutting-edge achievements in design methods and applications. First, the importance of $H_{\infty }$ SMC is explained with its primary perspectives. The motivation and contribution of this paper are then discussed in light of the lack of review works on the topic of interest. After that, the problem systems controlled using $H_{\infty }$ SMC and the challenges and perturbations included in each previous study are presented. In addition, the $H_{\infty }$ SMC design methods are qualitatively and quantitatively analyzed, with extensive critique reported for each. Figures and tables are provided for overall review. Finally, remaining issues and new study directions are provided to help scholars improve and grow the research subject. The observations of this review show that more contributions are needed to compensate different applications using further novel design methods.