An expansion of system with time delayed feedback control into spatio-temporal state space

Time delayed feedback control is well known as an effective continuous cont rol method for stabilizing the unstable periodic orbit embedded in chaotic attractors. As for the system with time delay, the solution is in a functio n space and shows characteristics governed by an infinite dimension. Theref ore it is difficult to understand the system behavior analytically. In this paper, it is shown that, when the state space for the system with time del ay is expanded into the spatio-temporal state space, the solution propagate s in the space as a wave theoretically and numerically. The dynamic behavio r experimentally obtained in the sinusoidally excited magneto-elastic beam system under time delayed feedback control is also discussed by the transfo rmation into the expanded spatio-temporal state space. (C) 1999 American In stitute of Physics. [S1054-1500(99)00104-4].