We discuss the enumeration theory for flags in Eulerian partially ordered sets, emphasizing
the two main geometric and algebraic examples, face posets of convex polytopes and …

This paper presents a set-membership based robust fault detection approach for mobile robots
with dynamic linear in some fault-related parameters. In the framework of set membership …

… 1A zonotope is the the Minkowski sum of line segments. 2Cooperative systems have a
monotonic behavior. In order to determine guaranteed upper and lower bounds, only calculations …

In this paper, a new approach to simulation of discrete linear time-invariant dynamic systems
with parameters and initial conditions described by fuzzy numbers is proposed. This …

Geometry is a classical core part of mathematics which, with its birth, marked the beginning
of the mathematical sciences. Thus, not surprisingly, geometry has played a key role in many …

The objective of this paper is to study a special family of Minkowski sums, that is of polytopes
relatively in general position. We show that the maximum number of faces in the sum can …

… 5] that use zonotopes and ellipsoids for representing parametric uncertainties. Linear
systems with polytopic uncertainties are also addressed in [9], where a gain matrix for a set-valued …

This paper presents a new ellipsoid bounding algorithm in the framework of the set-membership
filter for real-time state estimation of nonlinear systems with bounded-error assumptions…

… metrical representation such as polytopes or zonotopes. A reachability analyisis technique
targeted for phase-locked loops (PLLs) is developed recently [9]. One of the key ideas in the …

… of the segments [0, xi] between 0 and xi forms a zonotope which is a special polytope. Let
mn and let An D fx1,...,xmgn be the set of (n, n)-matrices with column vectors in fx1 ,..., x m g. …