Comparison of Reachability Methods for Uncertain LinearTime-Invariant Systems
In this paper, we evaluate a number of methods for computing reachable sets using on one hand approximations and on the other hand invariants. We address systems of the form x'(t)=Ax(t)+Bu(t) with uncertain but bounded input function u(t). We introduce our implementation based on zonotopes and use SpaceEx for support functions. Then, we go through our LMI-based implementation of ellipsoidal invariants and the canonical decomposition for large scale systems. Performance and accuracy of each method are evaluated using academic and practical examples.