Converting a continuous fuzzy signal by a linear dynamic system

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.