Solution of Fully Fuzzy Neutrosophic Lyapunov Matrix Equation

Abstract

 The classical Lyapunov matrix equation (LME) is important for checking system stability, but
it assumes we know exact numbers. It cannot handle unclear, conflicting, or missing information. Most of
real-world application of control systems have uncertainty and unpredictability that makes it hard to analyze
the stability precisely using conventional mathematical models. The classical Lyapunov matrix equation is
important in determining the system stability but it fails to accommodate vague, inconsistent, or incomplete
information. Therefore, this study introduces a solution for the Fully Fuzzy Neutrosophic Lyapunov Matrix
Equation (FFNLME) to address the limitation. The proposed model extends the classical model of LME into
the neutrosophic fuzzy domain by incorporating three independent membership components which are Truth
(T), Indeterminacy (I), and Falsity (F). Left right-triangular neutrosophic fuzzy numbers (LR-TriNFN) is
utilized to represent uncertain system parameters. Associated linear systems (ALS) and score function method
are employed for deneutrosophication, allowing for computational analysis while preserving the embedded un
certainty. The study demonstrates that the FFNLME framework provides a more comprehensive and flexible
representation of uncertain systems, enhancing the robustness of stability analysis compared to classical or
fuzzy Lyapunov equations. This formulation can be applied to both linear and nonlinear systems in control en
gineering, offering an effective means to evaluate stability under ambiguous or incomplete information. Future
research may focus on developing optimized numerical algorithms and extending this approach to large-scale
and time-varying systems

DOI 10.5281/zenodo.20091458