Stability of extended delayed-feedback control for discrete-time chaotic systems

The delayed-feedback control method has been utilized to stabilize real chaotic systems, since this method does not require a reference signal corresponding to a desired unstable periodic orbit. Ushio (1996) considered a discrete-time version of the delayed-feedback control system and derived a sufficient condition for the control system to be unstable. This paper analyzes the stability of the extended delayed-feedback control method proposed by Socolar et al. (1994). We derive simple instability conditions for the control system. To illustrate the conditions we give numerical examples.