Stability of conformable linear differential systems: a behavioural framework with applications in fractional‐order control

Abstract

The authors study the stability of linear systems whose dynamics are described by systems of conformable fractional differential equations. They provide a framework in terms of behavioural system theory to develop a general modelling specification as well as stability conditions for conformable linear systems with a fractional differential order. They also provide sufficient conditions and tests for stability based on linear matrix inequalities. To do so, they elaborate on the relationship between the conformable derivative and the traditional integer derivative as well as on a conformable Laplace transform and the use of polynomial algebra as the pivotal figure for analysis. They demonstrate the advantages of the proposed approach by designing a stabilising fractional-order controller for a DC–DC converter feeding a constant power load.