A generalized fractional Halanay inequality and its applications

TL;DR

This paper introduces a generalized Halanay inequality tailored for fractional-order delay systems, providing new stability estimates and practical criteria for fractional linear systems with delays.

Contribution

It develops a generalized Halanay inequality using Mittag-Leffler functions and applies it to derive stability conditions for fractional delay systems.

Findings

Established a generalized Halanay inequality for fractional systems

Derived optimal solution estimates for fractional delay systems

Provided numerical examples validating the theoretical results

Abstract

This paper is concerned with a generalized Halanay inequality and its applications to fractional-order delay linear systems. First, based on a sub-semigroup property of Mittag-Leffler functions, a generalized Halanay inequality is established. Then, applying this result to fractional-order delay systems with an order-preserving structure, an optimal estimate for the solutions is given. Next, inspired by the obtained Halanay inequality, a linear matrix inequality is designed to derive the Mittag-Leffler stability of general fractional-order delay linear systems. Finally, numerical examples are provided to illustrate the proposed theoretical results.