Invariant approximations of the minimal robust positively invariant set via finite time Aumann Integrals

This paper provides results on the minimal robust positively invariant set and its robust positively invariant approximations of an asymptotically stable, continuous-time, linear time-invariant system. The minimal robust positively invariant set is characterized as an infinite time Aumann Integral. A novel family of robust positively invariant sets, defined as a simple scaling of a finite time Aumann Integral, is characterized. Adequate members of this family are robust positively invariant sets and are arbitrarily close outer approximations of the minimal robust positively invariant set. A practical result, based on the optimal control theory, for the construction of safe polytopic sets is also provided. Computational procedures are briefly discussed and some simple, illustrative, examples are provided.