Stability criteria of nonlinear generalized proportional fractional delayed systems

TL;DR

This paper establishes new stability criteria for nonlinear generalized proportional fractional delayed systems, using inequalities and Mittag-Leffler functions, with numerical examples demonstrating their effectiveness.

Contribution

It introduces explicit finite time stability criteria for such systems, extending existing methods with novel analytical tools and inequalities.

Findings

Derived explicit stability criterion using Mittag-Leffler functions

Validated criteria through numerical simulations

Extended stability analysis to nonlinear delayed systems

Abstract

This work deals with the finite time stability of generalized proportional fractional systems with time delay. First, based on the generalized proportional Gr\"onwall inequality, we derive an explicit criterion that enables the system trajectories to stay within a priori given sets during a pre-specified time interval, in terms of the Mittag-Leffler function. Then, we investigate the finite time stability of nonlinear nonhomogeneous delayed systems by means of an approach based on H\"older's and Jensen's inequalities. Numerical applications are presented to illustrate the validity and feasibility of the developed results.