New matrix formulas for structural optical design have been obtained from analysis of derivative of the system matrix in respect to construction parameters and movements of components. Functional parameters of the optical system become elements of the matrix, presenting working conditions of the optical system. Developed methodology of structural design multi-group zoom systems with unlimited number of components and with mechanical-electronic compensation is presented. Any optical system, such as the objective lens, reproduction system, or telescopic system, can be analyzed with this methodology. Kinematics of components pertaining to a full tract of the zoom system is determined for a discrete number of positions. Three examples of the structural design of complex zoom systems with five-components and high zooming ratio are provided.
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