Stability analysis of electrical RLC circuit described by the Caputo-Liouville generalized fractional derivative

Abstract

We consider an electrical RLC circuit in two-dimensional spaces described by a fractional-order derivative. We propose the qualitative properties of the proposed model. We analyze the local asymptotic stability and the global asymptotic stability for the trivial equilibrium point for the electrical RLC circuit. We suggest the solution to the proposed model too. In our investigation, we consider the Caputo-Liouville fractional-order derivative. We use the characteristic matrix for the electrical RLC circuit model to analyze the local asymptotic stability of the trivial equilibrium point. For global asymptotic stability, we use the Lyapunov function method by constructing a Lyapunov function.