Modeling and stability analysis methods of neutrosophic transfer functions

  • Jun YeEmail author
  • Wenhua Cui
Methodologies and Application


Uncertainty is inherent property in actual control systems because parameters in actual control systems are no constants and changeable under some environments. Therefore, actual systems imply their indeterminate parameters, which can affect the control behavior and performance. Then, a neutrosophic number (NN) presented by Smarandache is very easy expressing determinate and/or indeterminate information because a NN p = c + dI is composed of its determinate term c and its indeterminate term dI for c, dR (R is all real numbers), where the symbol “I” denotes indeterminacy. Unfortunately, all uncertain modeling and analysis of practical control systems in existing literature do not provide any concept of NN models and analysis methods till now. Hence, this study firstly proposes a neutrosophic modeling method and defines a neutrosophic transfer function and a neutrosophic characteristic equation. Then, two stability analysis methods of neutrosophic linear systems are established based on the bounded range of all possible characteristic roots and the neutrosophic Routh stability criterion. Finally, the proposed methods are used for two practical examples on the RLC circuit and mass–spring–damper systems with NN parameters. The analysis results demonstrate the effectiveness and feasibility of the proposed methods.


Neutrosophic transfer function Neutrosophic characteristic equation Neutrosophic Routh stability criterion Neutrosophic characteristic root 



This paper was supported by the National Natural Science Foundation of China (No. 61703280).

Compliance with ethical standards

Conflict of interest

The authors declare that we have no conflict of interest regarding the publication of this paper.

Ethical approval

This article does not contain any studies with human participants performed by any of the authors.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Electrical and Information EngineeringShaoxing UniversityShaoxingPeople’s Republic of China

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