State estimation for nonlinear conformable fractional-order systems: A healthy operating case and a faulty operating case

The issue of estimating states for classical integer-order nonlinear systems has been widely addressed in the literature. Yet, generalization of existing results to the fractional-order framework represents a fertile area of research. Note that, recently, a new and advantageous type of fractional derivative, the conformable derivative, was defined. So far, the general query of designing observers for conformable fractional-order systems has not been investigated. In addition, it has been proved in the literature that some important tools for stability analysis of fractional-order systems are valid using the conformable derivative concept, but invalid using other fractional derivative concepts. Motivated by the cited facts, this paper presents a first-state estimation scheme for fractional-order systems under the conformable derivative concept. A healthy operating case and a faulty operating case are treated. In this paper, a version of Barbalat's lemma, which is invalid using the well-known Caputo derivative, is exploited to prove the convergence of the estimation errors. In order to validate the theoretical results, a numerical example is studied in the simulation section.