Segmented telescopes enable large-aperture space telescopes for the direct imaging and spectroscopy of habitable worlds. However, the increased complexity of their aperture geometry, due to their central obstruction, support structures, and segment gaps, makes high-contrast imaging very challenging. In this context, we present an analytical model that will enable to establish a comprehensive error budget to evaluate the constraints on the segments and the influence of the error terms on the final image and contrast. Indeed, the target contrast of 10^10 to image Earth-like planets requires drastic conditions, both in term of segment alignment and telescope stability. Despite space telescopes evolving in a more friendly environment than ground-based telescopes, remaining vibrations and resonant modes on the segments can still deteriorate the contrast. In this communication, we develop and validate the analytical model, and compare its outputs to images issued from end-to-end simulations.