Portable Electronic Systems are increasingly being sought by the company, either for leisure or for work. And this happens due to ease these devices bring to everyday life, and by their mobility, easy access to wireless networks, size, weight, functionality, among other. However, for their operation, portable electronic systems require a power source, the battery. Thus, this study seeks to find in the Theory of Identification Systems, a mathematical model to make the prediction of the lifetime of a battery. For this we conducted a literature review on batteries, on the state of the art of mathematical modeling to predict the lifetime of batteries and the Theory of System Identification. Later, was chosen a structure model of the Theory of System Identification, Auto Regressive model. Met the parameters of the model that fits the experimental data set obtained from a test platform, built for this purpose. The computational model was implemented using the software tool MATLAB and then held validation. The study with the Auto Regressive model showed good results.