Finite-time stability of nonlinear conformable fractional-order delayed impulsive systems: Impulsive control and perturbation perspectives

TL;DR

This paper establishes finite-time stability criteria for nonlinear conformable fractional-order delayed impulsive systems, considering impulsive control and perturbations, with applications to neural networks and simulations demonstrating effectiveness.

Contribution

It introduces novel Lyapunov-based FTS criteria for conformable fractional systems with delays and impulses, extending existing integer-order results to fractional-order frameworks.

Findings

Derived new FTS conditions for CFODISs

Estimated settling times under impulsive control and perturbations

Validated results through neural network simulations

Abstract

This paper investigates the finite-time stability (FTS) of nonlinear conformable fractional-order delayed impulsive systems (CFODISs). Using the conformable fractional-order (CFO) derivative framework, we derive a novel FTS result by extending the existing works on continuous integer-order (IO) systems. This result highlights that the settling time of continuous CFO systems depends on the system order and plays a crucial role in discussing FTS scenarios subject to delayed impulses. We establish Lyapunov-based FTS criteria for CFODISs, considering both impulsive control and impulsive perturbation. Additionally, we estimate the settling time for both cases, revealing distinct forms compared to the IO case. We apply the theoretical results to delayed impulsive conformable fractional-order memristive neural networks (CFOMNNs) under an elaborately designed controller. We present several simulations to illustrate the validity and applicability of our results.