Immersion and invariance control of a class of nonlinear cascaded discrete systems

This paper focuses on the control problem of nonlinear discrete systems. An immersion and invariance (I&I) based approach is introduced to stabilize nonlinear discrete systems, and then extended to chaotify nonlinear discrete systems. Its basic idea is to immerse a reduced order system (target system) which holds prespecified properties into the plant system and then to control the trajectories of the plant system to converge towards the invariant manifold where the target system is immersed. For a class of nonlinear cascaded discrete systems, we find that there exist corresponding one-dimensional systems such that these systems can be chaotified and stabilized through I&I design. An illustrating example with simulation results is presented to validate the proposed chaotification and stabilization algorithms. (C) 2015 Elsevier B.V. All rights reserved.