Fractional Order Hybrid Systems and Their Stability

TL;DR

This paper investigates the stability of fractional order hybrid systems, specifically switching and reset control systems, by extending Lyapunov methods and demonstrating their effectiveness through examples.

Contribution

It generalizes Lyapunov-based stability analysis methods for fractional order hybrid systems, including switching and reset control types, with new frequency domain criteria.

Findings

Generalized Lyapunov method for fractional switching systems

H$_{eta}$-condition for reset control systems

Validated methods with illustrative examples

Abstract

This paper deals with hybrid systems (HS) with fractional order dynamics and their stability. The stability of two particular types of fractional order hybrid systems (FOHS), i.e., switching and reset control systems, is studied. Common Lyapunov method, as well as its frequency domain equivalence, are generalized for the former systems and, for the latter, H$_{\beta}$-condition is used --frequency domain equivalence of Lyapunov-like method for reset control systems. The applicability and efficiency of the proposed methods are shown by some illustrative examples.