## A New Approach of Ordered Exponential in NMR: the Path-Sum

International audience

International audience

Applying algebraic and combinatorics techniques to solve graph problems leads to the birthof algebraic and combinatorial graph theory. This thesis deals mainly with a crossroads questbetween the two theories, that is, the problem of constructing infinite families of expandergraphs.From a combinatorial point of view, expander graphs are sparse graph...

The main aim of this thesis is to study the distributed tracking control problem for the multi-robot formation systems with nonholonomic constraint, of which the control objective it to drive a team of unicycle-type mobile robots to form one desired formation configuration with its centroid moving along with another dynamic reference trajectory, wh...

Published in International Journal of Control, Automation and Systems

Quasi average consensus of discrete time hybrid agents with heterogeneous dynamic nodes, i.e. the nodes with mixed first order and second order integrators is touched upon here. To be different from the already existing results, the consensus protocol for the hybrid order agents must be refined into two different sub protocols, one is for the first...

Published in Mathematical Geosciences

Evolution of Earth surface systems (ESS) comprises sequential transitions between system states. Treating these as directed graphs, algebraic graph theory was used to quantify complexity of archetypal structures, and empirical examples of forest succession and alluvial river channel change. Spectral radius measures structural complexity and is high...

© 2015 Elsevier B.V. Motivated by recent extensive studies on Wenger graphs, we introduce a new infinite class of bipartite graphs of a similar type, called linearized Wenger graphs. The spectrum, diameter and girth of these linearized Wenger graphs are determined.

Published in Journal of Algebraic Combinatorics

A Cayley graph for a group G is called normal edge-transitive if it admits an edge-transitive action of some subgroup of the holomorph of G [the normaliser of a regular copy of G in Sym(G)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usep...

Published in Nonlinear Dynamics

This paper studies the second-order consensus in multi-agent systems with sampled position and velocity data via pinning control. The distributed pinning consensus protocols with second-order dynamics are designed, where both sampled position and velocity data are employed. Necessary and sufficient conditions are derived for reaching second-order c...

Published in Linear Algebra and Its Applications

A recent result of one of the authors says that every connected subcubic bipartite graph that is not isomorphic to the Heawood graph has at least one, and in fact a positive proportion of its eigenvalues in the interval [−1,1]. We construct an infinite family of connected cubic bipartite graphs which have no eigenvalues in the open interval (−1,1),...

Published in Automatica

This paper discusses the design of distributed control gains for consensus in multi-agent systems with second-order nonlinear dynamics. First, an effective distributed adaptive gain-design strategy is proposed based only on local information of the network structure. Then, a leader–follower consensus problem in multi-agent systems with updated cont...