Control of systems with aftereffect in scales of linear controllers with respect to the type of feedback

For control systems with deviating argument, we consider basic problems of qualitative control theory such as problems of stabilization and modal control in scales of linear controllers with respect to the type of feedback, from the simplest difference controllers to integral controllers of general form. We analyze the results obtained in this direction. Special attention is paid to the stabilization of two-dimensional systems by feedback in the form of difference controllers. For the case in which the construction of a difference controller is impossible or too difficult, an integral feedback is used. Unlike the well-known Krasovskii-Osipov method for the construction of integral feedback in delay systems, the suggested method is based on the Paley-Wiener theorem for entire functions of exponential type.

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