Computation of invariant sets via immersion for discrete-time nonlinear systems

In this paper, we propose an approach for computing invariant sets of discrete-time nonlinear systems by lifting the dynamics into a higher dimensional linear model. particular, focus on maximal admissible set contained in some given constraint set. For special types systems, which can be exactly immersed with state transformations, original system characterized using representation. general without immersibility property, approximate immersions are defined local region within tolerance and approximations computed leveraging fixed-point iteration technique sets. Given bound mismatch between approximation system, provide inner tightening procedure.