Necessary and sufficient conditions for stabilizability of discrete-time systems via delayed feedback control

In this Letter, the stabilizability problem for single-input chaotic discrete-time systems under delayed feedback control (DFC) is completely solved. Necessary and sufficient conditions for stabilizability via DFC are obtained, which reveal the limitation of DFC more exactly than the odd number limitation. A nonlinear DFC is analytically designed for stabilizing a class of discrete-time systems at an unknown fixed point.