  This paper develops and implements an algorithm to compute sequences of
polytopic Robust Forward Invariant Sets (RFIS) that can parametrically vary in
size between the maximal and minimal RFIS of a nonlinear dynamical system. This
is done through a novel computational approach that geometrically deforms a
polytope into an invariant set using a sequence of homeomorphishms, based on an
invariance condition that only needs to be satisfied at a finite set of test
points. For achieving this, a fast computational test is developed to establish
if a given polytopic set is an RFIS. The geometric nature of the proposed
approach makes it applicable for arbitrary Lipschitz continuous nonlinear
systems in the presence of bounded additive disturbances. The versatility of
the proposed approach is presented through simulation results on a variety of
nonlinear dynamical systems in two and three dimensions, for which, sequences
of invariant sets are computed.
