Related papers: Finite-time consensus using stochastic matrices wi…
We analyze how the transient dynamics of large dynamical systems in the vicinity of a stationary point, modeled by a set of randomly coupled linear differential equations, depends on the network topology. We characterize the transient…
Several algorithms in prior literature have been proposed which guarantee consensus of normally behaving agents in a network that may contain adversarially behaving agents. These algorithms guarantee that the consensus value lies within the…
An emerging way of tackling the dimensionality issues arising in the modeling of a multivariate process is to assume that the inherent data structure can be captured by a graph. Nevertheless, though state-of-the-art graph-based methods have…
We consider a decentralized convex unconstrained optimization problem, where the cost function can be decomposed into a sum of strongly convex and smooth functions, associated with individual agents, interacting over a static or…
Imprecise continuous-time Markov chains are a robust type of continuous-time Markov chains that allow for partially specified time-dependent parameters. Computing inferences for them requires the solution of a non-linear differential…
This paper is concerned with the study of the stability of dynamical systems evolving on time scales. We first {formalize the notion of matrix measures on time scales, prove some of their key properties and make use of this notion to study…
We present a convergence result for infinite products of stochastic matrices with positive diagonals. We regard infinity of the product to the left. Such a product converges partly to a fixed matrix if the minimal positive entry of each…
We consider finite and infinite-dimensional first-order consensus systems with timeconstant interaction coefficients. For symmetric coefficients, convergence to consensus is classically established by proving, for instance, that the usual…
We consider the weight design problem for the consensus algorithm under a finite time horizon. We assume that the underlying network is random where the links fail at each iteration with certain probability and the link failures can be…
In this paper, we study the discrete-time consensus problem over networks with antagonistic and cooperative interactions. Following the work by Altafini [IEEE Trans. Automatic Control, 58 (2013), pp. 935--946], by an antagonistic…
We study the limit behaviour of a generally non-linear ordinary differential equation whose solution is a superadditive generalisation of a stochastic matrix, and provide necessary and sufficient conditions for this solution to be ergodic,…
The event-triggered consensus problem of first-order multi-agent systems under directed topology is investigated. The event judgements are only implemented at periodic time instants. Under the designed consensus algorithm, the sampling…
This paper discusses discrete-time maps of the form $x(k + 1) = F(x(k))$, focussing on equilibrium points of such maps. Under some circumstances, Lefschetz fixed-point theory can be used to establish the existence of a single locally…
A distributed average consensus algorithm in which every sensor transmits with bounded peak power is proposed. In the presence of communication noise, it is shown that the nodes reach consensus asymptotically to a finite random variable…
The effective resistance between a pair of nodes in a weighted undirected graph is defined as the potential difference induced between them when a unit current is injected at the first node and extracted at the second node, treating edge…
In this paper, we present new results on finite- and fixed-time convergence for dynamical systems using LaSalle-like invariance principles. In particular, we provide first and second-order non-smooth Lyapunov-like results for finite- and…
This paper addresses the distributed consensus problem for a linear multi-agent system with switching directed communication topologies. By appropriately introducing a linear transformation, the consensus problem is equivalently converted…
Consensus of autonomous agents is a benchmark problem in multi-agent control. In this paper, we consider continuous-time averaging consensus policies (or Laplacian flows) and their discrete-time counterparts over time-varying graphs in…
Given a set of well-formed terminal pairs on the external face of an undirected planar graph with unit edge weights, we give a linear-time algorithm for computing the union of non-crossing shortest paths joining each terminal pair, where…
We establish general conditions under which there exists uniform in time convergence between a stochastic process and its approximated system. These standardised conditions consist of a local in time estimate between the original and the…