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We present an algorithm for a time-delayed feedback control design tostabilize periodic orbits with an odd number of positive Floquet exponents inautonomous systems. Due to the so-called odd number theorem such orbits havebeen considered as uncontrollable by time-delayed feedback methods. However,this theorem has been refuted by a counterexample and recently a correctedversion of the theorem has been proved. In our algorithm, the control matrix isdesigned using a relationship between Floquet multipliers of the systemscontrolled by time-delayed and proportional feedback. The efficacy of thealgorithm is demonstrated with the Lorenz and Chua systems.

Time-Delayed Feedback Control Design Beyond the Odd Number Limitation