%0 Journal Article %A Khlopin, Dmitriy V. %D 2004 %I Begell House %N 7 %P 17-30 %R 10.1615/JAutomatInfScien.v36.i7.30 %T On Extremal Step-by-Step Realization of Sliding Modes %U https://www.dl.begellhouse.com/journals/2b6239406278e43e,30ebd6066e9a2820,1d63179c7cd5e62c.html %V 36 %X For a controllable differential system uniform approximation of sliding modes was considered by means of trajectories generated by piecewice-constant controls. The conditions of solution uniqueness associated with each control were not imposed. Two discrete rules of extremal shift were investigated. It was shown that 1) by a discrete version of Kryazhimskii method one can approximate some trajectories of the bundle generated by the given generalized control; 2) there exist generalized trajectories which are not approximated by admissible trajectories; 3) if the controllable system satisfies the conditions of Kanke general uniqueness theorem, then any arbitrary sliding mode is approximated by Krasovskiy extremal shift rule. %8 2004-07-01