Interpolation, box splines, and lattice points in zonotopes

M Lenz - International Mathematics Research Notices, 2014 - ieeexplore.ieee.org
Let X be a totally unimodular list of vectors in some lattice. Let B X be the box spline defined
by X. Its support is the zonotope Z(X). We show that any real-valued function defined on the …

Set-membership state estimation for discrete time piecewise affine systems using zonotopes

SM Tabatabaeipour, J Stoustrup - 2013 European Control …, 2013 - ieeexplore.ieee.org
This paper presents a method for guaranteed state estimation of discrete time piecewise
affine systems with unknown but bounded noise and disturbance. Using zonotopic set …

[HTML][HTML] On the sum of a parallelotope and a zonotope

MD Sikirić, V Grishukhin, A Magazinov - European Journal of …, 2014 - Elsevier
… parallelotope P and a zonotope Z ( U ) , where U is the set of vectors used to generate the
zonotope. In this … Using this we classify such zonotopes for some highly symmetric lattices. …

An asynchronous technique for distributed estimation based on zonotopes

RA García, FR Rubio, M Guinaldo… - … Conference on Event …, 2015 - ieeexplore.ieee.org
This paper deals with the problem of guaranteed distributed estimation under an asynchronous
communication scheme. The objective is to estimate the state of a perturbed linear plant …

A zonotope-based method for capturing the effect of variable generation on the power flow

X Jiang, AD Domínguez-García - 2014 North American Power …, 2014 - ieeexplore.ieee.org
… this zonotope through a linearized model of the power system. The result is a zonotope
system static performance, we verify that this zonotope is contained within the region of the static …

[HTML][HTML] Illumination complexes, Δ-zonotopes, and the polyhedral curtain theorem

RT Živaljević - Computational Geometry, 2015 - Elsevier
… Δ-zonotopes R Δ Generalizing and developing the ideas from Section 2 we introduce Δ-zonotopes
as higher dimensional analogues of the centrally symmetric hexagon, used in the …

Polar root polytopes that are zonotopes

P Cellini, M Marietti - arXiv preprint arXiv:1502.06377, 2015 - arxiv.org
… and call Zonp(S) the zonotope generated by S with center p. Thus a zonotope in U is a … We
prove that, for An and Cn, the polar root polytope P∗ is the zonotope generated by the orbit of …

Zonotope-based nonlinear model order reduction for fast performance bound analysis of analog circuits with multiple-interval-valued parameter variations

Y Song, MPD Sai, H Yu - 2014 Design, Automation & Test in …, 2014 - ieeexplore.ieee.org
zonotope-based model for multiple-interval-valued parameter variations. As such, one can
have a zonotope-… to approximate a number of zonotopes along the set of trajectories, one can …

Congruence and metrical invariants of zonotopes

E Gover - arXiv preprint arXiv:1401.4749, 2014 - arxiv.org
… The defining matrix A of a zonotope Z(A) ⊂ Rn determines the zonotope as both … zonotope
is also a convex polytope with centrally symmetric faces in all dimensions. When a zonotope

A CSP versus a zonotope-based method for solving guard set intersection in nonlinear hybrid reachability

M Maïga, N Ramdani, L Travé-Massuyès… - … in Computer Science, 2014 - Springer
… For completeness, we overview a preliminary version of an algorithm based on solving a
CSP, then we introduce a variant using zonotopes. These two methods will be compared on the …