Unstable periodic orbits in certain chaotic systems may be stabilized via small perturbations of a control parameter. Stabilization using linear feedback has been achieved in both simulations and physical experiments. Not all chaotic systems can be controlled easily or well, and the effectiveness of proposed control algorithms depends strongly on mathematical properties of the chaotic behavior. Practical considerations are discussed that affect the robustness of local linear control strategies, with emphasis on the range of feedback gains which can stabilize the linearized map.
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Bayly et al. (1994) studied this question.
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