This paper will discuss the stability of a system constituted by a DC/DC converter supplying a DC microgrid on which is connected a tightly controlled device behaving as a Constant Power Load with its low damped LC input filter. The input filter cutoff frequency can be high in transportation systems where small passive components are employed. The dynamic behavior of the entire system in high frequency range is often not studied with the classical tools based on average modeling. Here, the system is modeled by a discrete-time model of the converter including control variables. The impact of the LC filter on the stability of the system is investigated. Moreover, a stabilizer is designed to extend the stability domain. Experimental results, conducted on a laboratory test-bench are given in order to validate the proposed model and stabilizer.