Full characterization on limitation of generalized delayed feedback control for discrete-time systems

In this paper, the stabilizability problem for chaotic discrete-time systems under the generalized delayed feedback control (GDFC) is addressed. It is proved that 0 < det(I − A) < 2n+m is a necessary and sufficient condition of stabilizability via m-step GDFC for an n-order system with Jacobi A. The condition reveals the limitation of GDFC more exactly than the odd number limitation. An analytical procedure of designing GDFC is proposed and illustrated by an example.