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Zonotopes are becoming an increasingly popular set representation for formal verification techniques.
A note on a method for generating points uniformly on n-dimensional spheres
M. E. Muller · 1959
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An algebra of polygons through the notion of negative shapes
P. K. Ghosh · 1991
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Approximating the ball by a Minkowski sum of segments with equal length
J. Bourgain and J. Lindenstrauss · 1993
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Approximation of zonoids by zonotopes in fixed directions
S. Campi, D. Haas, and W. Weil · 1994
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Lectures on Polytopes
G. M. Ziegler · 1995
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Some results about Minkowski addition and difference
L. Montejano · 1996
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The n-dimensional cross product and its application to the matrix eigenanalysis
D. Mortari · 1996
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Theory and computation of disturbance invariant sets for discrete-time linear systems
I. Kolmanovsky and E. G. Gilbert · 1998
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Mathematical Visualization
W. Kühn · 1998
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Rigorously computed orbits of dynamical systems without the wrapping effect
W. Kühn · 1998
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Coherence and enumeration of tilings of 3-zonotopes
G. D. Bailey · 1999
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Cores of cooperative games, superdifferentials of functions, and the Minkowski difference of sets
V. I. Danilov and G. A. Koshevoy · 2000
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Ellipsoidal techniques for reachability analysis
A. B. Kurzhanski and P. Varaiya · 2000
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Collision prediction and avoidance amidst moving objects for trajectory planning applications
E. J. Bernabeu, J. Tornero, and M. Tomizuka · 2001
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Zonotopes associated with higher Bruhat orders
S. Felsner and G. M. Ziegler · 2001
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Robust interval regression analysis based on Minkowski difference
M. Inuiguchi, H. Fujita, and T. Tanino · 2002
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Optimal control of constrained, piecewise affine systems with bounded disturbances
E. C. Kerrigan and D. Q. Mayne · 2002
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Guaranteed state estimation by zonotopes
T. Alamo, J. M. Bravo, and E. F. Camacho · 2003
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Computational techniques for hybrid system verification
A. Chutinan and B. H. Krogh · 2003
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A state bounding observer based on zonotopes
C. Combastel · 2003
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Frequently asked questions in polyhedral computation, 2004
K. Fukuda · 2004
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From the zonotope construction to the Minkowski addition of convex polytopes
K. Fukuda · 2004
Cited alongside, same era.
Handbook of Discrete and Computational Geometry
M. Henk, J. Richter-Gebert, and G. M. Ziegler · 2004
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A state bounding observer for uncertain non-linear continuous-time systems based on zonotopes
C. Combastel · 2005
Cited alongside, same era.
Solving the fixed rank convex quadratic maximization in binary variables by a parallel zonotope construction algorithm
J.-A. Ferrez, K. Fukuda, and T .M. Liebling · 2005
Cited alongside, same era.
A logical product approach to zonotope intersection
K. Ghorbal, E. Goubault, and S. Putot · 2010
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Determinants and the volumes of parallelotopes and zonotopes
E. Gover and N. Krikorian · 2010
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Reachable set computation for uncertain time-varying linear systems
M. Althoff, C. Le Guernic, and B. H. Krogh · 2011
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On positive invariance for delay difference equations
W. Lombardi, S. Olaru, M. Lazar, and S.-I. Niculescu · 2011
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Reachability analysis of nonlinear systems using conservative polynomialization and non-convex sets
M. Althoff · 2013
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Multi-parametric toolbox 3.0
M. Herceg, M. Kvasnica, C.N. Jones, and M. Morari · 2013
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Reachability of uncertain linear systems using zonotopes
A. Girard · 2005
Cited alongside, same era.
Zonotopes as bounding volumes
L. J. Guibas, A. Nguyen, and L. Zhang · 2005
Cited alongside, same era.
A time-dependent Hamilton–Jacobi formulation of reachable sets for continuous dynamic games
I. M. Mitchell, A. M. Bayen, and C. J. Tomlin · 2005
Cited alongside, same era.
Robust MPC of constrained discrete-time nonlinear systems based on approximated reachable sets
J. M. Bravo, T. Alamo, and E. F. Camacho · 2006
Cited alongside, same era.
Efficient computation of reachable sets of linear time-invariant systems with inputs
A. Girard, C. Le Guernic, and O. Maler · 2006
Cited alongside, same era.
Static analysis of numerical algorithms
E. Goubault and S. Putot · 2006
Cited alongside, same era.
Zonotopes: From Guaranteed State-estimation to Control
V. T. H. Le, C. Stoica, T. Alamo, E. F. Camacho, and D. Dumur · 2013
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Zonotopic guaranteed state estimation for uncertain systems
V. T. H. Le, C. Stoica, T. Alamo, E. F. Camacho, and D. Dumur · 2013
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Reachability analysis of nonlinear differential-algebraic systems
M. Althoff and B. H. Krogh · 2014
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An introduction to CORA 2015
M. Althoff · 2015
Closest in time.
A verified algorithm for geometric zonotope/hyperplane intersection
F. Immler · 2015
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On computing the Minkowski difference of zonotopes
M. Althoff · 2016
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Methods for order reduction of zonotopes
A.-K. Kopetzki, B. Schürmann, and M. Althoff · 2017
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A comparison of zonotope order reduction techniques
X. Yang and J. K. Scott · 2018
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Linear encodings for polytope containment problems
Sadra Sadraddini and Russ Tedrake · 2019
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Set propagation techniques for reachability analysis
M. Althoff, G. Frehse, and A. Girard · 2021
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Comparison of guaranteed state estimators for linear time-invariant systems
M. Althoff and J. J. Rath · 2021
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Set operations and order reductions for constrained zonotopes
Vignesh Raghuraman and Justin P. Koeln · 2022
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