Reachability analysis of linear systems with uncertain parameters and inputs

Abstract — For a dynamic system with given initial state set, the reachable state set contains the states along all possible trajectories defined over (in-)finite time. This paper presents a method for computing conservative approximations of reach-able sets for linear systems with uncertain system matrices and bounded inputs. Over- and underapproximations 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. I