Estudo da estabilidade de circuitos RC via otimização

Abstract

Study of non-linear RC network stability. An RC network is considered assymptotically stable when the capacitar charges converge to equilibrium charges. The study is developed from the analysis of the behavior of resistive networks. It is assumed that all resistors have increasing characteristics curves, from which it is possible to formulate resistive network problems as optimization problems on graphs. Duality techniques are used in the proof of certain results. Additional hypothesis on the resistors, depending on the network structure, will permit representation of the networks solutions as solutions of a system of differential equations for which the existence and uniqueness of solutions is guaranteed. Liapunov's method is the basic tool in the stability analysis of this system of equations.