Abstract
Linear dynamical systems are researched under the conditions of incompleteness of information on their initial condition. The functions of the condition of the systems under consideration are constructed, which, being the solutions of a linear differentially defined mathematical model of the system, are coordinated according to the root-mean square criterion with the available observations for it. According to this criterion also the control problems of the considered system by the combination of the initial and current external dynamical perturbations are solved. The accuracy of the obtained solutions is evaluated and conditions of their unambiguousness are formulated.
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