Chaotification of nonlinear discrete systems via immersion and invariance

This paper is concerned with the chaotification of nonlinear discrete systems. A novel method based on (system) immersion and (manifold) invariance (I&I) is introduced to chaotify nonlinear discrete systems. Its basic idea is to immerse an ideal system which holds chaotic properties and may be a lower dimension into the plant system, and then control trajectories of the plant system to converge toward the invariant manifold where the ideal system is immersed. For a class of linearizable systems, we present the immersion and the control law such that these systems can be chaotified through I&I design. An illustrative example with simulation is presented to validate the proposed chaotification scheme.