Laurent Truffet

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In this paper, the interrelation between positive invariance, monotonicity and comparison of iterated nonlinear systems defined in partially ordered sets is studied. First, necessary and sufficient conditions guaranteeing the positive invariance of sets defined by relations of the form v(x) ≤ w with respect to nonlinear systems are established. Then,(More)
In this paper, we develop an approach to compare two discrete-time Markov chains which are not assumed to have the same state space. To do this, we introduce a binary relation between probability vectors or marginal laws which is not a partial order in general. This binary relation generalizes the notion of stochastic ordering for discrete random variables(More)
In this paper we show that the so-called array Fréchet problem in Probability/Statistics is (max,+)-linear. The upper bound of Fréchet is obtained using simple arguments from residuation theory and lattice distributivity. The lower bound is obtained as a loop invariant of a greedy algorithm. The algorithm is based on the max-plus linearity of the Fréchet(More)
Haar’s Lemma (1918) deals with the algebraic characterization of the inclusion of polyhedral sets. This Lemma has been involved many times in automatic control of linear dynamical systems via positive invariance of polyhedrons. More recently, it has been used to characterize stochastic comparison w.r.t. linear/integral ordering of Markov (reward) chains. In(More)