Robust stability for fractional-order systems with structured and unstructured uncertainties

TL;DR

This paper develops less conservative and necessary conditions for the robust stability of uncertain fractional-order systems, applicable to polytope and norm-bounded uncertainties, verified through numerical examples.

Contribution

It introduces new stability criteria for fractional-order systems with structured and unstructured uncertainties, improving upon existing methods.

Findings

Less conservative stability conditions for polytope uncertainties

Necessary and sufficient conditions for norm-bounded uncertainties

Numerical examples confirm the effectiveness of the proposed criteria

Abstract

The issues of robust stability for two types of uncertain fractional-order systems of order $\alpha \in (0,1)$ are dealt with in this paper. For the polytope-type uncertainty case, a less conservative sufficient condition of robust stability is given; for the norm-bounded uncertainty case, a sufficient and necessary condition of robust stability is presented. Both of these conditions can be checked by solving sets of linear matrix inequalities. Two numerical examples are presented to confirm the proposed conditions.