In this paper we discuss numerical strategies to find periodic orbits of nonlinear dynamic system. These orbits shall be open-loop stable and robust with respect to bounded disturbances. For this aim, we review and extend existing techniques from the field of reachability analysis and ellipsoidal calculus to compute robust positive invariant tubes for nonlinear dynamic systems. We suggest a conservative approximation strategy for robust stability optimization providing guarantees on the region of attraction. The technique is tested by applying it to an inverted spring pendulum for which robust and open-loop stable orbits exist.
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