Abstract. The possibility to obtain a finite decay time of free process in a linearized model of a digital track-ing system using a linear discrete correction device is demonstrated. The decay time does not exceed the integer number of sampling periods equal to the order of the system continuous part, and therefore the maximum possible speed of the system is achieved. The conditions of free process damping for fi-nite time are derived: controllability and observability of the discrete model of the continuous part of the system. To comply with the conditions, the absence of common multipliers of the numerator and denom-inator of the transfer function of the continuous part is necessary. The method of choice of the simplest transfer function of the discrete correcting device considering requirements of system roughness is pro-posed. An example of a digital tracking system with a continuous part of the 3rd order is analyzed.

Keywords: digital tracking system, free process, finite decay time

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