Analyzing Reachability of Linear Dynamic Systems with Parametric Uncertainties

Abstract As an important approach to analyzing safety of a dynamic system, this paper considers the task of computing overapproximations of reachable sets, i.e. the set of states which is reachable from a given initial set of states. The class of systems under investigation are linear, time-invariant systems with parametric un-certainties and uncertain but bounded input. The possible set of system matrices due to uncertain parameters is represented by matrix zonotopes and interval matrices – computational techniques for both representations are presented. The reachable set is represented by zonotopes, which makes it possible to apply the approach to sys-tems of 100 continuous state variables with computation times of a few minutes. This is demonstrated for randomized examples as well as a transmission line exam-ple.