Geodesic
Converting a continuous fuzzy signal by a linear dynamic system
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXV", Voronezh, April 26-30, 2024, Part 3, Tome 237 (2024), pp. 34-48

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In this paper, we apply the method of Green's function to the search for bounded solutions of a high-order linear differential equation with constant coefficients and a fuzzy right-hand side. A class of equations with positive coefficients and a nonnegative Green's function is distinguished, for which the results on the existence and smoothness of a fuzzy solution bounded on the whole axis are established. We prove that in the case where the right-hand side has a triangular form, the solution has the same form. Examples of radio engineering circuits with fuzzy input signals are considered.
Keywords: fuzzy-valued functions, fuzzy dynamical systems with a constant coefficient, Green's function method. 
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     author = {V. L. Khatskevich},
     title = {Converting a continuous fuzzy signal by a linear dynamic system},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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     publisher = {mathdoc},
     volume = {237},
     year = {2024},
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}
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V. L. Khatskevich. Converting a continuous fuzzy signal by a linear dynamic system. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXV", Voronezh, April 26-30, 2024, Part 3, Tome 237 (2024), pp. 34-48. http://geodesic.mathdoc.fr/item/INTO_2024_237_a3/