Modeling and stability analysis methods of neutrosophic transfer functions

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, d ∈ R (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.