Abstract
In this chapter, new results on the state estimation problem for fractional-order systems are presented. First, a robust observer scheme for a class of linear fractional systems with matched uncertainties is proposed. Then, a novel observer design for nonlinear fractional-order systems is given. This observer is applied for both nonlinear Lipschitz systems and nonlinear One-Sided Lipschitz systems. In the rest of this chapter, the specific problem of robust state estimation for fractional One-Sided Lipschitz systems, in the presence of unknown inputs, is tackled. A particular form of observers, namely the Unknown Input Observer, is used to accomplish this task. In this context, a full-order observer version, as well as a reduced-order observer version, are detailed and analysed.
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Naifar, O., Jmal, A., Ben Makhlouf, A., Derbel, N., Hammami, M.A. (2022). State Estimation for Fractional-Order Systems. In: Naifar, O., Ben Makhlouf, A. (eds) Fractional Order Systems—Control Theory and Applications. Studies in Systems, Decision and Control, vol 364. Springer, Cham. https://doi.org/10.1007/978-3-030-71446-8_4
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