The article deals with the development of mathematical description of systems for stabilization of measurement and observation equipment assigned for operation at moving vehicles of the wide class such as land, marine, and air moving vehicles. Mathematical descriptions of one-axis, two-axis, and three-axis stabilization systems are represented including kinematical relations and dynamics models. The general mathematical descriptions and the appropriate models in the space of states are given. The basic approaches to linearization of the generalized models are represented. The sets of turns in the inertial space for two-axial and three-axial stabilizations systems are represented. The obtained mathematical model for one-axis stabilization system has been used for the robust structural synthesis of the system assigned for stabilization of the observation equipment mounted at the land moving vehicles. The obtained results can be spread on moving vehicles of the different type.