ANALYTICAL TREATMENT OF DELAYED FEEDBACK-CONTROL

The stabilization of unstable periodic orbits by means of time-delayed feedback mechanisms is treated analytically on the basis of new metho ds which appear as a generalization of results from the theory of ordi nary differential equations. We derive explicit expressions for the Fl oquet exponents which govern the linear stability of the controlled or bit. The analytical method is applied to the Lorenz-Haken equations de scribing single mode laser dynamics. We compare our analytical results with numerical simulations and present a significant extension of the original time-delayed control mechanism. (C) 1998 Elsevier Science B. V.