Small LC filters connected to tightly controlled power loads may lead to instabilities. With small LC filters comes a high cutoff frequency, and the conventional stability analysis based on an average model may not be precise enough. Other tools based on another model are required to study this type of system. In this paper, a new discrete-time model is proposed to investigate the behavior of the studied system and to take into account the switching effect. Then, the stability analysis of the limit cycle is done using Floquet multipliers. This system is composed of a dc-dc boost converter, an LC filter, and a controlled power load. Simulation and experimental results are given to validate the proposed model and analysis.