Multiple Delayed Feedback Control of Discrete-time Quasi-periodic Orbits*

The multiple delayed feedback control (MDFC) is proposed for stabilizing discrete-time quasi-periodic orbits (QPOs). There is an inevitable difference between the current and past states in QPOs. In the MDFC, we estimate the current state by the interpolation method using the multiple past states. We apply the MDFC to the sampled-data control of a continuous-time periodic orbit, because the sampled time series is quasi-periodic if the sampling duration is rationally independent of the period of the periodic orbit.