Analysis of signals, audio and video information

Application of Cauchy function in the problem of transforming a fuzzy signal by linear dynamic system

V. L. Khatskevich

N. E. Zhukovsky and Y. U. Gagarin Air Force Academy, Voronezh, Russia

Abstract: The problem of transforming a fuzzy signal by a linear dynamic system is investigated. Within the framework of this problem, the application of the Cauchy function method to solving the initial value problem for a high-order linear differential equation with variable coefficients and a fuzzy-valued right-hand side is developed. A class of equations with positive coefficients and a non-negative Cauchy function is identified, for which results on the existence and smoothness of a fuzzy solution to the initial value problem are established. It is shown that in the case of a triangular right-hand side, the solution will be of the same type. As an application, a model of a radio engineering circuit (a series oscillatory circuit) with a fuzzy input signal is considered. The results of the proposed article can find application in problems of signal analysis and transformation, evolutionary modeling, and optimal control of linear objects.

Keywords: fuzzy-valued functions, fuzzy linear differential equations with variable coefficients, Cauchy function method.

DOI: 10.14357/20718594250209

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