A Unified KKL-based Interval Observer for Nonlinear Discrete-time Systems

This work proposes an interval observer design for nonlinear discrete-time systems based on the Kazantzis-Kravaris/Luenberger (KKL) paradigm. Our design extends to generic nonlinear systems without any assumption on the structure of its dynamics and output maps. Relying on a transformation putting the system into a target form where an interval observer can be directly designed, we then propose a method to reconstruct the bounds in the original coordinates using the bounds in the target coordinates, thanks to the Lipschitz injectivity of this transformation achieved under Lipschitz distinguishability when the target dynamics have a high enough dimension and are pushed sufficiently fast. An academic example serves to illustrate our methods.