Comparison of reachability methods for uncertain linear time-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 ẋ(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.