The study of the positive invariance and contractivity properties of polyhedral sets with respect to (w.r.t) linear systems subject to control saturation is addressed. The analysis of the nonlinear behavior of the closed-loop saturated system is made by dividing the state space in regions of saturation. In each one of these regions, the system evolution can be represented by the that of a linea...

Let a polyhedral convex set be given by a finite number of linear inequalities and consider the problem to project this set onto a subspace. This problem, called polyhedral projection problem, is shown to be equivalent to multiple objective linear programming. The number of objectives of the multiple objective linear program is by one higher than the dimension of the projected polyhedron. The r...

We analyze the asymptotic convergence of all infinite products of matrices taken in a given finite set by looking only at finite or periodic products. It is known that when the matrices of the set have a common nonincreasing polyhedral norm, all infinite products converge to zero if and only if all infinite periodic products with periods smaller than a certain value converge to zero. Moreover, ...

This paper presents deployment strategies for a team of multiple mobile robots with line-of-sight visibility in 1.5D and 2.5D terrain environments. Our objective is to distributively achieve full visibility of a polyhedral environment. In the 1.5D polyhedral terrain, we achieve this by determining a set of locations that the robots can distributively occupy. In the 2.5D polyhedral terrain, we a...

We present an algorithm for computing shortest paths and distances from a single generalized source (point, segment, polygonal chain or polygon) to any query point on a possibly non-convex polyhedral surface. The algorithm also handles the case in which polygonal chain or polygon obstacles on the polyhedral surface are allowed. Moreover, it easily extends to the case of several generalized sour...

We show that Nash equilibrium components are universal for the collection of connected polyhedral sets. More precisely for every polyhedral set we construct a so-called binary game—a common interest game whose common payoff to the players is at most equal to one—whose success set (the set of strategy profiles where the maximal payoff of one is indeed achieved) is homeomorphic to the given polyh...