Hybrid Systems and Control With Fractional Dynamics (I): Modeling and Analysis

TL;DR

This paper introduces the fundamentals of fractional-order hybrid systems, focusing on modeling and stability analysis of switching and reset control systems, aiming to enhance system design flexibility.

Contribution

It pioneers the integration of hybrid and fractional-order system theories, providing a foundational framework for modeling and stability analysis.

Findings

Developed models for fractional-order switching systems

Analyzed stability conditions for fractional reset control systems

Illustrated the applicability with relevant examples

Abstract

No mixed research of hybrid and fractional-order systems into a cohesive and multifaceted whole can be found in the literature. This paper focuses on such a synergistic approach of the theories of both branches, which is believed to give additional flexibility and help to the system designer. It is part I of two companion papers and introduces the fundamentals of fractional-order hybrid systems, in particular, modeling and stability analysis of two kinds of such systems, i.e., fractional-order switching and reset control systems. Some examples are given to illustrate the applicability and effectiveness of the developed theory. Part II will focus on fractional-order hybrid control.