Whitney numbers of arrangements via measure concentration of intrinsic volumes

KA Adiprasito, R Sanyal - arXiv preprint arXiv:1606.09412, 2016 - arxiv.org
… We prove that the associated convex bodies (zonotopes for hyperplane arrangements,
discotopes for c-arrangements) have a Wills polynomial resembling the characteristic polynomial …

Reachability analysis of nonlinear differential-algebraic systems

M Althoff, BH Krogh - IEEE Transactions on Automatic Control, 2013 - ieeexplore.ieee.org
… Besides zonotopes, support functions have been shown to be … systems, so we use zonotopes
since they can be used for … order of zonotopes to ρ = 400 and the order of zonotopes for the …

[PDF][PDF] Shuffles of deformed permutahedra, multiplihedra, constrainahedra, and biassociahedra

F Chapoton, V Pilaud - Preprint - lix.polytechnique.fr
… In this paper, we will anyway only need Minkowski sums of graphical zonotopes of graphs
with disjoint edge sets. Finally, we briefly describe the graphical zonotopes of complete …

[HTML][HTML] Determination of the available wrench set of a 3-RPRR kinematically-redundant planar parallel manipulator

M Arsenault, R Boudreau, S Nokleby - Mechanism and Machine Theory, 2022 - Elsevier
… specified by ρ is a zonotope in the wrench space. The AWS of the robot at x , ie W ,
corresponds to the union of the infinite number of W ρ zonotopes that are obtained as the leg …

Adaptive event-triggered finite-frequency fault detection with zonotopic threshold analysis for LPV systems

J Wang, Z Wang, M Zhou - IEEE Transactions on Cybernetics, 2021 - ieeexplore.ieee.org
… Next, the upper and lower bounds of the generated residual are calculated by the zonotope
… Based on the characteristics of the zonotope and system variables, we can obtain the …

Robust Feedback Motion Primitives for Exploration of Unknown Terrains

C Chernik, P Tajvar, J Tumova - 2021 IEEE/RSJ International …, 2021 - ieeexplore.ieee.org
zonotopes to represent the reachable sets as they are closed under linear transformations;
ie starting from a zonotope set Zx in the state space and having a zonotope … using zonotopes

Direct Computing on Control Capability for Linear Continuous-time Systems Based on Hurwitz Matrix

M Zhao - arXiv preprint arXiv:2210.08483, 2022 - arxiv.org
… volume computing method for the smooth controllability zonotope for the linear continuoustime(…
Because the controllability zonotope and ellipsoid are directly related to control capability …

[HTML][HTML] A zonotopic set-invariance analysis of replay attacks affecting the supervisory layer

C Trapiello, V Puig, D Rotondo - Systems & Control Letters, 2021 - Elsevier
… Among the possible set representations, zonotopes will be employed in this paper due to …
the invariant sets are represented as zonotopes. Conditions to guarantee attack detectability …

Zonotope 表現を用いたハイブリッドシステムの可到達性解析

小木曽公尚 - 自動制御連合講演会講演論文集 第 52 回自動制御連合 …, 2009 - jstage.jst.go.jp
… reachable set in a zonotope for a continuous-time linear system with a switching plane, which
has been proposed in [3,4]. An interesting point is that the zonotope is closed under linear …

Robust fault diagnosis using parallelotope-based set-membership consistency tests

A Ingimundarson, JM Bravo, V Puig… - Proceedings of the 44th …, 2005 - ieeexplore.ieee.org
… One of the principal features of zonotopes is that the Minkowski sum of a box and a zonotope
is another zonotope. Therefore, if at time k it is known that the parameter belongs to set Zk …