Constructing invariants sets of pre-specified complexity, for systems subject to non-convex constraints

Many practical problems in control and safety analysis can be recast as invariant set computation problems. For this reason, several well-established approaches for invariant set constructions can be found in the literature, mainly stemming from Lyapunov theory or reachability analysis. However, even for the case of linear or switched-linear systems, there still remain questions that have not been fully answered: How do we compute invariant sets that have a bounded complexity in their description and a non-trivial size? How do we compute the domain of attraction for systems subject to semi-algebraic constraints? We will try to address the first question by introducing a new geometric expansion procedure. To address the second question, we will utilize algebraic liftings which eventually transform non-convex constraints into polyhedral ones.