.png){kind=icon}
.png){kind=icon}
Return
Mittag–Leffler stability of mild solutions of ψ-Caputo fractional-order time-delay systems and applications
.png){kind=icon}
PRE
AI
N
T
L
DOI：10.1016/j.jfranklin.2026.108712.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
In this paper, a class of fractional-order time-delay systems described by ψ-Caputo fractional derivative is studied. The concept of mild solutions, a type of integral solutions or generalized solutions, is presented and the existence and uniqueness of (mild) solutions is explored using the Banach fixed point theorem. Then, by utilizing the properties of Mittag–Leffler functions and novel comparison techniques, Mittag–Leffler stability of mild solutions is addressed. The proposed conditions are derived in both the spectral-type conditions (which can be extended to fractional-order systems in infinite dimensional Hilbert spaces) and matrix inequality-type conditions. As an application, tractable conditions to design problem of a state-feedback controller are also obtained. The derived stability conditions are then validated by given numerical examples.
Keywords:
Mittag–Leffler stability
ψ-Caputo fractional derivative
time-delay systems
mild solutions
fractional-order systems
Journal
J
IF:
4.2
Papers:
812
Citations:
0
Organization
No organization information available
Cited Papers