A new nonlinear discrete-time observer design method with linearizable error dynamics

The present research study provides a concrete set of conditions under which a nonlinear discrete-time observer exists that induces linear estimation error dynamics for nonlinear discrete-time continuous (C0) systems. The problem under consideration is mathematically addressed through the existence of a homeomorphism in the state space that maps the orbits of a linear system with an output injection onto the observing system, which indicates the existence of an invariant attracting manifold for the extended system. Within this framework, the discrete-time version of the well-known Hartman-Grobman Theorem can be naturally reproduced as a special case. The performance of the proposed nonlinear discrete-time observer is evaluated using a nonlinear dynamical chaotic system of the Lozi-type.