Finite-Interval Stability Analysis of Impulsive Fractional-Delay Dynamical System

Stability analysis over a finite time interval is a well-formulated technique to study the dynamical behaviour of a system. This article provides a novel analysis on the finite-time stability of a fractional-order system using the approach of the delayed-type matrix Mittag-Leffler function. At first, we discuss the solution's existence and uniqueness for our considered fractional model. Then standard form of integral inequality of Gronwall's type is used along with the application of the delayed Mittag-Leffler argument to derive the sufficient bounds for the stability of the dynamical system. The analysis of the system is extended and studied with impulsive perturbations. Further, we illustrate the numerical simulations of our analytical study using relevant examples.

Automated summary

This article provides a novel analysis on the finite-time stability of a fractional-order system using the approach of the delayed-type matrix Mittag-Leffler function. The existence and uniqueness of the solution for the considered fractional model are discussed first. Then, the standard form of integral inequality of Gronwall's type is used along with the application of the delayed Mittag-Leffler argument to derive the sufficient bounds for the stability of the dynamical system. The analysis of the system is extended and studied with impulsive perturbations, and numerical simulations are illustrated using relevant examples.