We study stability of slow oscillatory motions in first order one- and two-dimensional systems with delayed relay control element and periodic disturbances, which serve as models of stabilization of the fingers of an underwater manipulator and of control of fuel injectors in automobile engines. Various types of stability observed are used to design a direct adaptive control of relay type with time delay that extinguishes parasite auto-oscillations in these models. [S0022-0434(00)04004-1]

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