scholarly journals Leader-Following Consensus in Networks of Agents with Nonuniform Time-Varying Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Zhao-Jun Tang ◽  
Ting-Zhu Huang ◽  
Jiang-Ping Hu ◽  
Jin-Liang Shao
Keyword(s):  
Sufficient Condition ◽  
Time Varying ◽  
Consensus Problem ◽  
Communication Delays ◽  
Necessary And Sufficient Condition ◽  
Leader Following ◽  
Fixed Topology ◽  
Simulation Results ◽  
Necessary And Sufficient ◽  
Theoretical Results

This paper is concerned with a leader-following consensus problem for networks of agents with fixed and switching topologies as well as nonuniform time-varying communication delays. By employing Lyapunov-Razumikhin function, a necessary and sufficient condition is derived in the case of fixed topology, and a sufficient condition is obtained in the case when the interconnection topology is switched and satisfies certain condition. Simulation results are provided to illustrate the theoretical results.

scholarly journals Impulsive Consensus for Leader-Following Multiagent Systems with Fixed and Switching Topology

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Zhi-Wei Liu ◽  
Zhi-Hong Guan ◽  
Hong Zhou
Keyword(s):  
Multiagent System ◽  
Impulsive Control ◽  
Sampling Period ◽  
Switching Topology ◽  
Sufficient Condition ◽  
Leader Following ◽  
Fixed Topology ◽  
The Stability ◽  
Sampling Instant ◽  
Necessary And Sufficient

This paper studied the consensus problem of the leader-following multiagent system. It is assumed that the state information of the leader is only available to a subset of followers, while the communication among agents occurs at sampling instant. To achieve leader-following consensus, a class of distributed impulsive control based on sampling information is proposed. By using the stability theory of impulsive systems, algebraic graph theory, and stochastic matrices theory, a necessary and sufficient condition for fixed topology and sufficient condition for switching topology are obtained to guarantee the leader-following consensus of the multiagent system. It is found that leader-following consensus is critically dependent on the sampling period, control gains, and interaction graph. Finally, two numerical examples are given to illustrate the effectiveness of the proposed approach and the correctness of theoretical analysis.

scholarly journals Study of “Sticking and Restarting Phenomenon” in Electropneumatic Positioning Systems

2005 ◽  
Vol 127 (1) ◽  
pp. 173-184 ◽  
Author(s):  
Xavier Brun ◽  
Sylvie Sesmat ◽  
Daniel Thomasset ◽  
Serge Scavarda
Keyword(s):  
Dry Friction ◽  
Partial Equilibrium ◽  
Experimental Result ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Pressure Force ◽  
Friction Forces ◽  
Positioning Systems ◽  
Necessary And Sufficient ◽  
Theoretical Results

This paper explains the possible occurrence of the “sticking and restarting phenomenon” observed with electropneumatic positioning systems. This is carried out from the notion of partial equilibrium, with the analysis of the model which incorporates two parallel phenomena which are used to generate a pressure force subjected to dry friction forces. Also, an experimental result has been studied in a particular pressure force plane which shows the origin of the problem more explicitly. The theoretical results give a necessary and sufficient condition for the restarting phenomenon not to occur and, if this condition is not validated, there is an estimation of the restarting time. Understanding this undesirable phenomenon will be the basis for further work which will attempt to find solutions to avoid its occurrence.

scholarly journals Consensus of Discrete Time Second-Order Multiagent Systems with Time Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Wei Zhu
Keyword(s):  
Time Delay ◽  
Convergence Rate ◽  
Theoretical Result ◽  
Multiagent Systems ◽  
Discrete Time ◽  
Second Order ◽  
Sufficient Condition ◽  
Consensus Problem ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

The consensus problem for discrete time second-order multiagent systems with time delay is studied. Some effective methods are presented to deal with consensus problems in discrete time multiagent systems. A necessary and sufficient condition is established to ensure consensus. The convergence rate for reaching consensus is also estimated. It is shown that arbitrary bounded time delay can safely be tolerated. An example is presented to illustrate the theoretical result.

scholarly journals Synchronization of a Generalized High-dimensional Kuramoto Model With Directed Graphs

2021 ◽  
Author(s):  
Jinxing Zhang ◽  
Jiandong Zhu ◽  
Xiaodi Li
Keyword(s):  
Directed Graph ◽  
Directed Graphs ◽  
Kuramoto Model ◽  
High Dimensional ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Initial State ◽  
Necessary And Sufficient ◽  
Theoretical Results

Abstract In this paper, a generalized high-dimensional Kuramoto model with directed graphs is investigated. A necessary and sufficient condition for equilibria is given and the synchronization is proved under weaker directed graph conditions and more general initial state constrains. Finally, an example is given to validate the theoretical results.

scholarly journals Multivaluedness in Networks: Theory

2020 ◽  
Author(s):  
Anton van Wyk
Keyword(s):  
Structural Complexity ◽  
The Other ◽  
Sufficient Condition ◽  
The Novel ◽  
Necessary And Sufficient Condition ◽  
Cascaded Systems ◽  
The Right ◽  
Necessary And Sufficient ◽  
Theoretical Results

<div>An unexpected and somewhat surprising observation is that two counter-cascaded systems,12 satisfying the right conditions, implicitly exhibit multivaluedness from one of the outputs to the other. Based on the novel notions of immanence and transcendence, the main result presented here, gives a necessary and sufficient condition for multivaluedness to be exhibited by counter-cascaded systems. Subsequent corollaries provide further characterization of multivaluedness under specific conditions.</div><div><br></div><div>As an application of these theoretical results, we demonstrate how these aid in the structural complexity reduction of directed complex networks.</div>

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