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The observer design problem for integer-order systems has been the subject of several studies. However, much less interest has been given to the more general fractional-order systems, where the fractional-order derivative is between 0 and 1. In this paper, a particular form of observers for integer-order Lipschitz, one-sided Lipschitz and quasi-one-sided Lipschitz systems, is extended to the fractional-order calculus. Then, the obtained states estimates are used for an eventual feedback control, and the separation principle is tackled. The effectiveness of the proposed scheme is shown through simulation for two numerical examples.

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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.