Analyzing Potential Source Response of the Stochastic Differential Equation of RLC Circuit driven by Lyapunov Techniques

Abstract

In this paper, we delve into the investigation of the necessary condition for the stochastic stability of an RLC circuit by employing the Lyapunov method, a rigorous mathematical approach widely utilized in dynamical systems analysis. Beyond merely identifying stability criteria, we delve deeper into understanding the behavioral intricacies inherent in the circuit's dynamics. To provide a comprehensive analysis, we manually derive the range of parameter values that satisfy the stability criterion, ensuring accuracy and reliability. Additionally, we implement PYTHON coding to computationally confirm our findings, thereby validating the analytical results with numerical simulations. The culmination of our efforts is visually represented through a graph, effectively showcasing the consistent outcomes obtained from both analytical and computational methodologies.