Stability and passivity analysis of nonlinear RLC circuits

In this study, the stability and passivity of the systems are discussed in detail both in theory and in practice. Some nonlinear electrical circuits and mechanical systems in the literature have been selected as applications; stability, global asymptotic stability (GAS) and passivity of these systems have been examined by using Lyapunov's direct (second) method. A convenient Lyapunov function was constructed for each nonlinear system examined. In addition, the relationship between the energies and passivity of the systems has been demonstrated using Lyapunov functions. Moreover, it has been proved that stability and passivity analyzes can be performed by modeling mathematical models of different types of dynamic systems to electrical circuits. For each system analyzed, simulations of the results were obtained by using MATLAB program and these simulations were compared with the theoretical results.