Integro-differential equations are widely used in mathematical modeling of various phenomena from biology, physics and other sciences. The article deals with linear controlled objects described by linear integro-differential equations. The main object of the study is the attainable sets of such controlled objects and some of their properties. In particular, it is considered the continuous dependence in the Hausdoff metric of the attainable sets for small deviations in special norms of matrix functions that determine the dynamics of the controlled object under consideration.
Note that the study of the properties of attainable sets of linear and nonlinear controlled objects is an important problem in modern control theory .
Keywords : linear integro-differential equations, controlled objects, attainable sets, Hausdorff metric
Received July 28, 2026
Revised August 10, 2026
Accepted August 17, 2026
Mikhail Sergeevich Nikol’skii, Dr. Phys.-Math. Sci., Prof., Leading Researcher, Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia, e-mail: mni@mi-ras.ru
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Cite this article as: M.S. Nikol’skii. A note about linear controlled integro-differential equations. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2026, vol. 32, no. 3, pp. 176–182.
