Introduction of sliding mode control and fractional-order control systems

The primary objective of this chapter is to provide readers with a comprehensive understanding of the historical origins and fundamental concepts of fractional calculus theory. It endeavors to delve into the intricate interplay between fractional calculus and its practical applications, particularly focusing on the implementation of fractional sliding mode control theory and event-triggered mechanisms across a diverse array of fractional-order systems. These systems encompass fractional-order chaotic systems, fractional-order coupled systems, and fractional-order multi-agent systems. Through an in-depth exploration of fractional sliding mode control design principles, the chapter aims to elucidate how these advanced methodologies can be effectively applied. Additionally, the chapter offers a curated selection of references to pertinent literature, aimed at enriching the scholarly discourse and stimulating further exploration in the field.