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On vibrational stabilizability of nonlinear systems. (English) Zbl 0548.93063
Conditions of vibrational stabilizability for trivial solutions of nonlinear systems are derived. Several examples based on the classical equations of the theory of oscillations are given.

MSC:
93D15 Stabilization of systems by feedback
70K20 Stability for nonlinear problems in mechanics
93C10 Nonlinear systems in control theory
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems, general theory
70K40 Forced motions for nonlinear problems in mechanics
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[1] Meerkov, S. M.,Principle of Vibrational Control: Theory and Applications, IEEE Transactions on Automatic Control, Vol. AC-25, pp. 755-762, 1980. · Zbl 0454.93021 · doi:10.1109/TAC.1980.1102426
[2] Meerkov, S. M.,Condition of Vibrational Stabilizability for a Class of Nonlinear Systems, IEEE Transactions on Automatic Control, Vol. AC-27, pp. 485-487, 1982. · Zbl 0491.93034 · doi:10.1109/TAC.1982.1102897
[3] Bellman, R., Bentsman, J., andMeerkov, S. M.,Vibrational Control of Systems with Arrhenius Dynamics, Journal of Mathematical Analysis and Applications, Vol. 91, pp. 152-191, 1983. · Zbl 0525.93034 · doi:10.1016/0022-247X(83)90099-9
[4] Bogoliubov, N. N., andMitropolsky, Yu. A.,Asymptotic Methods in the Theory of Nonlinear Oscillations, Gordon and Breach, New York, New York, 1961.
[5] Leitmann, G.,The Calculus of Variations and Optimal Control, Plenum Press, New York, New York, 1981. · Zbl 0475.49003
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