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Approach to Solve the Problems of Filtration and Extrapolation in the Construction of Functionally Stable Stochastic Systems with Delay

Filtration and interpolation problems play an important role in the theory of complex technical object control. To improve the operating efficiency control of these objects, it is necessary to improve the mathematical models of the control objects. A large number of objects can be attributed to stochastic discrete objects with limited delay and, under a priori uncertainty, to stochastic discrete objects with unlimited delay as well. It is important to substantiate the application of stochastic analysis methods to solve problems of filtration and interpolation of systems with delay. The problem of conditionally optimal filter design is substantiated.