Testing Local Lorentz Invariance with high-accuracy astrometric observations

This paper summarizes the analysis of the consequences of the violation of the Local Lorentz Invariance (LLI) on astrometric observations. We demonstrate that from the point of view of the LLI astrometric observations represent an experiment of Michelson-Morley type. The future high-accuracy astrometric projects (e.g., Gaia) will be used to test the LLI.