A generalization of delayed feedback control in chaotic discrete-time systems

Pyragas proposes (1992) a practically useful control method, called delayed feedback, for control of chaos. Conditions for (local) stabilization by the delayed feedback, however, are more restricted than those by the OGY method. In order to overcome this problem, we proposed a delayed feedback control method using nonlinear estimation of stabilized orbits. Moreover, we give necessary and sufficient conditions for local stabilization of fixed points by the proposed method, using linear matrix inequalities, and obtain a parameterization of all feedback gains stabilizing the fixed points.