Reachability analysis of linear systems with uncertain parameters and inputs

For a dynamic system with given initial state set, the reachable state set contains the states along all possible trajectories defined over (in-)flnite time. This paper presents a method for computing conservative approximations of reachable sets for linear systems with uncertain system matrices and bounded inputs. Over- and under-approximations are computed for exponentials of system matrices with entries specified as bounded intervals. It is shown that reachable sets represented by sequences of zonotopes can be computed up to a dimension of 100 within a few seconds.