… using zonotopes. From these zonotopes, an interval for each state variable can also be
obtained by computing the interval hull of the zonotope. The sequence of interval hulls DXe …

… By adding the vector ξ3 = (1,1) the matrix M defines a mesh inside a zonotope, as shown in
… that is the sum of the vectors in V , or the zonotope with V as the set of its generators. The …

… zonotopes using an algorithm based on the one proposed by [6]. From these zonotopes, an
… obtained by computing the interval hull of the zonotope. The sequence of interval hulls DXe …

… of vertices of any zonotope and on the algorithmic complexity of constructing its vertices,
each vertex along with a linear functional maximized over the zonotope uniquely at that vertex. …

… fan of the zonotope with the arrangement. If F is a face of A, then, let ˆF denote the corresponding
face of the zonotope. Each face ˆF is an affine translate of a zonotope of a closed sub- …

… The reachability problem in hybrid automata is also a field close to our work: for instance,
the tool SpaceEx [13] uses zonotopes to compute guaranteed set of trajectories, ie bounding …

… , such as boxes 6, parallelotopes 7, zonotopes 8 or other limited-complexity polytopes. Matlab
… based on the description of sets by zonotopes, where again IA plays an important role 20. …

… Vast improvement in over-approximated reachability set computation efficiencies has been
realized for linear systems using zonotopes [11] and support functions [12]. Similar work has …

This thesis is devoted to the problem of computing reachable sets of linear and hybrid
systems. In the first part, after exposing existing approaches for reachability analysis of linear …

… The lower bound in Theorem 1.1 is asymptotically tight: it is attained, up to a multiplicative
constant factor, by the following zonotope Z, which is equivalent to the member M2 …