Fractional Order Hybrid Systems and Their Stability
It provides theoretical stability tools for fractional order hybrid systems, which are important for control engineers working with such systems, but the results are incremental extensions of existing methods.
The paper extends stability analysis methods to fractional order hybrid systems, specifically switching and reset control systems, by generalizing the common Lyapunov method and Hβ-condition, with illustrative examples demonstrating applicability.
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$_β$-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.