A nonlinear control scheme for discrete time chaotic systems

Abstract

In this paper we consider the stabilization problem of unstable periodic orbits of discrete time chaotic systems. We consider both one dimensional and higher dimensional cases. We propose a nonlinear feedback law and present some stability results. These results show that for period 1 all hyperbolic periodic orbits can be stabilized with the proposed method. By restricting the gain matrix to a special form we obtain some novel stability results. The stability proofs also give the possible feedback gains which achieve stabilization. We also present some simulation results.