Lyapanov Stability Analysis of Neutrosophic Descriptor System with Time-Varying Delays.

Source abstract

In this paper, we discuss the exponential stability (in the Lyapunov sense) of descriptor systems (differential-algebraic equations) with time-varying delays under neutrosophic uncertainty. Descriptor systems have arisen naturally in many engineering applications, including robotics and mechanical systems. The presence of parametric uncertainties and time delays lead to complications in stability analysis. Neutrosophic logic can be characterized by three independent components: truth (T), falsehood (F) and indeterminacy (I). This logic provides a robust framework for modeling uncertainties. In this work, we propose a neutrosophic descriptor system where all matrices take the form A(t+zI)=A_0(t)+A_I(t), where A_0(t) is the crisp matrix and A_I(t) is the indeterminacy matrix. Based on this, a new Lyapunov-Krasovskii functional will be constructed, and sufficient conditions for exponential stability will be derived in terms of linear matrix inequalities (LMIs) (independent of the specific value of I) and will be applied, ensuring the robustness of the proposed method. To reinforce the theoretical aspect, we will give an example based on RLC circuit that illustrates the methodology.