A criterion for asymptotic stability of general fractional-order linear time-invariant systems with incommensurate orders

TL;DR

This paper introduces a new stability criterion for fractional-order linear systems with incommensurate orders, accommodating real-valued uncertain parameters and simplifying stability analysis.

Contribution

It provides a novel, low-complexity method to determine stability regions in parameter space for fractional systems with incommensurate orders.

Findings

Determines boundary of stable parameter regions.

Decomposes parameter space into finitely many stable/unstable regions.

Requires only one point check per region for stability.

Abstract

A criterion on the asymptotic stability of fractional-order systems with incomensurate orders is proposed in this paper. Existing methods always assume order parameters be rational numbers or the ratios of any two orders be rational numbers. In engineering applications, order parameters are more likely to be uncertain which may be real numbers. Furthermore, the boundary of the stable parameter region is determined, which decomposes parameter space into the finite number of connected regions. All systems whose parameters belong to the same region have the same stability. Each region only needs checking one point to determine the stability of the region. The method established in this paper involves low computational complexity and clearly gives the relationship between order parameters and stability. Some examples show the advantages of this method.