Local control lyapunov functions for constrained linear discrete-time systems: The minkowski algebra approach

SV Rakovic, M Baric - IEEE Transactions on Automatic Control, 2009 - ieeexplore.ieee.org
… and S is a zonotope with q generators and since the number of generators of a set/zonotope
S1 8S2 is upper bounded by q1 +q2 when S1 and S2 are zonotopes with q1 and q2 …

Specialties of Models of the 6-dimensional Cube

L Vörös - … of Bridges 2010: Mathematics, Music, Art …, 2010 - archive.bridgesmathart.org
We can have several procedures to construct 3-dimensional models of the more-dimensional
cubes and 2-dimensional shadows of these, even on the classical field of Platonic and …

On the design of Robust tube-based MPC for tracking

D Limón Marruedo, I Alvarado Aldea, T Alamo… - 2008 - idus.us.es
This paper deals with the design procedure of the recently presented robust MPC for
tracking of constrained linear systems with additive disturbances. This controller is based on …

k-Parabolic Subspace Arrangements

J White, C Severs - Discrete Mathematics & Theoretical …, 2009 - dmtcs.episciences.org
… Recall that we can associate a zonotope to a hyperplane arrangement. That … zonotope is
called the W-Permutahedron. Also, the fan of the arrangement is the normal fan of the zonotope. …

[HTML][HTML] On dissimilarity and opportunity equalization

F Andreoli - 2012 - search.proquest.com
… Our result links Zonotopes inclusion with the existence of a sequence of dissimilarity
preserving/reducing operations, as the Lorenz curve is related to the existence of a sequence of …

Geometry of the restricted Boltzmann machine

MA Cueto, J Morton, B Sturmfels - Algebraic Methods in Statistics …, 2010 - books.google.com
… Likewise, the third entry in (5.2) and (5.3) refers to a 4-dimensional zonotope with 40
facets and λ (3)= 104 vertices. The normal fan of that zonotope is an arrangement of eight …

k-Parabolic Subspace Arrangements

C Severs, J White - Discrete Mathematics and Theoretical Computer …, 2009 - hal.inria.fr
… Recall that we can associate a zonotope to a hyperplane arrangement. That … zonotope is
called the W-Permutahedron. Also, the fan of the arrangement is the normal fan of the zonotope. …

Hierarchical zonotopal spaces

O Holtz, A Ron, Z Xu - Transactions of the American Mathematical Society, 2012 - ams.org
… In other words, the zonotope Z(X) is the image of the unit cube … as zonotopes, zonotope
tilings, lattice points in zonotopes, … ideals to the zonotope Z(X) and to several other constructs. …

SpaceEx: Scalable verification of hybrid systems

G Frehse, CL Guernic, A Donzé, S Cotton… - … on Computer Aided …, 2011 - Springer
We present a scalable reachability algorithm for hybrid systems with piecewise affine, non-deterministic
dynamics. It combines polyhedra and support function representations of …

Drawing polytopal graphs with polymake

E Gawrilow, M Joswig, T Rörig, N Witte - Computing and visualization in …, 2010 - Springer
… data defining a zonotope). These 3-zonotopes are remarkable since naively one might expect
only a linear number of vertices in any section of a “typical” 3-dimensional zonotope. Their …