On the existence and stabilization of an upper unstable limit cycle of the damped forced pendulum

Bánhelyi, Balázs and Csendes, Tibor and Hatvani, László (2019) On the existence and stabilization of an upper unstable limit cycle of the damped forced pendulum. Computational and Applied Mathematics. ISSN 2238-3603 (In Press)

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Abstract

By the use of intervalmethods it is proven that there exists an unstable periodic solution to the damped and periodically forced pendulum around the upper equilibrium. It is also proved that this solution can be stabilized by a control which does not need the knowledge of values of the state variables but of the unstable periodic solution.

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