Further clarifications of "Necessary and sufficient stability condition of fractional-order interval linear systems"

TL;DR

This paper clarifies the stability conditions for fractional-order interval systems, correcting previous misinterpretations and confirming the established condition as an exact criterion for quadratic stability.

Contribution

It provides detailed clarifications and corrections to prior work, establishing the stability condition as an exact criterion for quadratic stability in fractional-order interval systems.

Findings

The established condition is an exact criterion for quadratic stability.

Clarification of the relationship between robust and quadratic stability.

Correction of misinterpretations in previous stability analyses.

Abstract

This technical report replies to the comments of [2] in detail, and corrects a possible mis-interpretation of [1] in terms of the conventional robust stability concept. After defining the robust stability and quadratic stability concepts, it will be more clearly described that the condition established in [1] can be considered an exact condition for the quadratic stability of fractional-order interval systems.