Second Order Approximation of Reachable Sets of LTI Systems

We present a novel method to approximate reachable sets at time points, of continuous-time LTI systems, in which initial states are subject to compact convex uncertainty and the input may arbitrarily vary over time within a zonotopic uncertainty set. We prove a priori bounds on the approximation error, which are of second order depending on a discretization parameter and can be used to subsequently obtain overand under-approximations rather than mere approximations. In contrast to competing approaches, our method does not iteratively propagate over-or under-approximations, and it does not reduce the complexity of any of the zonotopes internally produced at intermediate stages. We compare the performance of our method to that of competing approaches on examples.