We establish a compensator design via the separation principle in the practical sense for a class of semi-linear evolution equations in Hilbert spaces. Under a restriction imposed on the perturbation, which is bounded by an integrable function, we propose a nonlinear time-varying practical Luenberger observer to estimate the states of the system and prove that the Luenberger observer based on a linear controller stabilizes the system. An illustrative example is given to demonstrate the applicability of our theoretical results.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 8, pp. 1073–1085, August, 2022. Ukrainian DOI:https://doi.org/10.37863/umzh.v74i8.6152.
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Damak, H. Compensator Design Via the Separation Principle for a Class of Semilinear Evolution Equations. Ukr Math J 74, 1225–1239 (2023). https://doi.org/10.1007/s11253-023-02131-8
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DOI: https://doi.org/10.1007/s11253-023-02131-8