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- Laurent Truffet
- IMA J. Math. Control & Information
- 2004

- George Bitsoris, Laurent Truffet
- Systems & Control Letters
- 2011

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)

- Laurent Truffet
- POSTA
- 2003

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)

We study linear systems in the max-plus algebra, where the basic operations are maximum and addition. We define a preorder to compare the state vectors of maxplus linear systems with the same dimension. We provide two algebraic methods to get bounds (with respect to this preorder) on the state vectors of a lumped maxplus linear system. The first method is… (More)

- Mourad Ahmane, Laurent Truffet
- ICINCO-SPSMC
- 2006

- L. TRUFFET
- 2009

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)

- Laurent Truffet, Edouard Wagneur
- Discrete Applied Mathematics
- 2005

- Mourad Ahmane, Laurent Truffet
- Kybernetika
- 2007

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)

- Mourad Ahmane, Laurent Truffet
- ASMTA
- 2009