Design and robustness of delayed feedback controllers for discrete systems
A matrix form of time-delay feedback control in the context of discrete time maps of high dimension was studied. Time-delay feedback controllers containing only static elements can be designed to achieve identical linear stability properties, in almost all cases where standard proportional feedback control methods can achieve control. This control was a generalization of a method called 'extended time-delay autosynchronization' (ETDAS). Analysis of an example involving a ring of coupled maps that can be controlled at only two sites demonstrated that the time-delay controller equivalent to a standard optimal controller can be equally robust in the presence of noise.