Geodesic
Use of finite-dimensional approximations in a~problem of stabilization of periodic systems with aftereffect
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2015), pp. 29-45

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We consider a stabilization problem for linear periodic system of differential equations with aftereffect. Approximating systems are described by differential equations with finite-dimensional Volterra operators. We construct admissible controls by feedback principle in a class of piecewise continuous functions. We obtain a relation between approximating problem of stabilization and a problem of optimal stabilization of autonomous linear system of difference equations.
Keywords: stabilization, systems of linear periodic differential equations with aftereffect, approximating operators, feedback control. 
@article{IVM_2015_1_a2,
     author = {Yu. F. Dolgii and E. V. Koshkin},
     title = {Use of finite-dimensional approximations in a~problem of stabilization of periodic systems with aftereffect},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {29--45},
     publisher = {mathdoc},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2015_1_a2/}
}
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Yu. F. Dolgii; E. V. Koshkin. Use of finite-dimensional approximations in a~problem of stabilization of periodic systems with aftereffect. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2015), pp. 29-45. http://geodesic.mathdoc.fr/item/IVM_2015_1_a2/