Stability of fractional-order linear time-invariant system with noncommensurate orders

TL;DR

This paper establishes stability conditions for fractional-order LTI systems with noncommensurate orders, providing necessary and sufficient criteria and illustrating results through numerical inverse Laplace transform techniques.

Contribution

It introduces the first comprehensive stability criteria for fractional-order systems with multiple noncommensurate orders, expanding existing theoretical frameworks.

Findings

Derived necessary and sufficient stability conditions.

Validated stability criteria with numerical inverse Laplace transform.

Analyzed systems with double noncommensurate orders.

Abstract

Bounded-input bounded-output stability conditions for fractional-order linear time-invariant (LTI) system with multiple noncommensurate orders have been established in this paper. The orders become noncommensurate orders when they do not have a common divisor. Sufficient and necessary conditions of stability for this kind of fractional-order LTI system with multiple noncommensurate orders. Based on the numerical inverse Laplace transform technique, time-domain responses for a fractional-order system with double noncommensurate orders are presented to illustrate the obtained stability results.