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Local Lyapunov Functions for Consensus in Switching Nonlinear Systems

Johan Thunberg, Xiaoming Hu, Jorge Goncalves
2017 IEEE Transactions on Automatic Control  
For such systems, instead of proving consensus by using the theory of contracting convex sets, a local quadratic Lyapunov function can be used. , where he is currently a professor of Optimization and Systems  ...  This note presents two theorems on asymptotic state consensus of continuous time nonlinear multi-agent systems. The agents reside in R m and have switching interconnection topologies.  ...  Both theorems introduce local Lyapunov-like functions, guaranteeing consensus in multi-agent systems.  ... 
doi:10.1109/tac.2017.2652302 fatcat:nhwizgc7tnc2tluv5vzbsoq6au

Second-Order Consensus Seeking in Multi-Agent Systems With Nonlinear Dynamics Over Random Switching Directed Networks

Huaqing Li, Xiaofeng Liao, Xinyu Lei, Tingwen Huang, Wei Zhu
2013 IEEE Transactions on Circuits and Systems Part 1: Regular Papers  
This paper discusses the second-order local consensus problem for multi-agent systems with nonlinear dynamics over dynamically switching random directed networks.  ...  Several sufficient conditions for reaching almost surely second-order local consensus are derived for the cases of time-delay-free coupling and time-delay coupling, respectively.  ...  ACKNOWLEDGMENT The authors are very grateful to the associate editor and anonymous reviewers for their constructive comments based on which the presentation of the paper has been greatly improved.  ... 
doi:10.1109/tcsi.2012.2226507 fatcat:z6b2rantmbeltmkglxlm6qylcu

Nonlinear Multi-Agent System Consensus with Time-Varying Delays

Ulrich Münz, Antonis Papachristodoulou, Frank Allgöwer
2008 IFAC Proceedings Volumes  
for Lyapunov-Razumikhin functions.  ...  In this paper, we provide conditions for a nonlinear, locally passive MAS with timevarying communication delays to reach a consensus, using a recently presented method based on an invariance principle  ...  In this paper, we present a continuous-time consensus protocol for nonlinear, locally passive MAS with delayed exchange of information.  ... 
doi:10.3182/20080706-5-kr-1001.00260 fatcat:6d6lwvsdefcq3drp2ywqznvhku

Nonlinear Analysis of Dynamical Complex Networks

Zidong Wang, Bo Shen, Hongli Dong, Jun Hu
2013 Abstract and Applied Analysis  
Complex networks have already become an ideal research area for control engineers, mathematicians, computer scientists, and biologists to manage, analyze, and interpret functional information from real-world  ...  Sophisticated computer system theories and computing algorithms have been exploited or emerged in the general area of computer mathematics, such as analysis of algorithms, artificial intelligence, automata  ...  Acknowledgments This special issue is a timely reflection of the research progress in the area of nonlinear analysis of dynamical complex networks.  ... 
doi:10.1155/2013/530124 fatcat:k2qk6lytnvdcdlkjq6mpga7pya

On local synchronisability of nonlinear networked systems with a unit inner-coupling matrix and switching topology

Ji Xiang, Wei Wei
2011 International Journal of Control  
The local synchronization of the nonlinear networked systems with switching topology has been studied in this paper for the special case in which the inner coupling matrix is a unit matrix.  ...  A novel local synchronous criterion consisting of the maximum Lyapunov exponent of nodal self-dynamics and the consensus convergent rate of the switching topology is given.  ...  Local synchronization of networked systems with the fast and periodic switching topology has been investigated in Ref.  ... 
doi:10.1080/00207179.2011.625044 fatcat:kzckidic6reopohocenvy7j4ey

An Extension of LaSalle's Invariance Principle and Its Application to Multi-Agent Consensus

Daizhan Cheng, Jinhuan Wang, Xiaoming Hu
2008 IEEE Transactions on Automatic Control  
Index Terms-LaSalle's invariance principle, multi-agent consensus, switched linear systems, weak common quadratic Lyapunov function.  ...  Unlike most existing results in which each switching mode in the system needs to be asymptotically stable, this paper allows that the switching modes are only Lyapunov stable.  ...  ACKNOWLEDGMENT The authors would like to thank an anonymous reviewer for the very detailed comments on the proof of the main result.  ... 
doi:10.1109/tac.2008.928332 fatcat:r7acru4xvjgq3c2immarrovdam

Effects of Delay in Multi-Agent Consensus and Oscillator Synchronization

Antonis Papachristodoulou, Ali Jadbabaie, Ulrich Münz
2010 IEEE Transactions on Automatic Control  
In this paper, we consider what effect multiple, noncommensurate (heterogeneous) communication delays can have on the consensus properties of large-scale multi-agent systems endowed with nonlinear dynamics  ...  We show that the structure of the delayed dynamics allows functionality to be retained for arbitrary communication delays, even for switching topologies under certain connectivity conditions.  ...  In particular the Lyapunov-Razumikhin function used for the delayed case (8) is the same as the Lyapunov function (4) used for the undelayed system.  ... 
doi:10.1109/tac.2010.2044274 fatcat:bgsvmouuvbdi5crpoi77qqustu


Leonid Fridman, Denis Efimov, Salah Laghrouche
2021 International Journal of Robust and Nonlinear Control  
Existence of Lyapunov functions in the same class of homogeneous maps hints a way for their selection.  ...  for a class of single-input-single-output uncertain nonlinear systems. 3376  ...  Pisano present a research "On the fixed-time consensus problem for nonlinear uncertain multiagent systems under switching topology" suggested local interaction rule providing leader-following and leader-less  ... 
doi:10.1002/rnc.5549 fatcat:dgsjorxk2faqjktrnoafdt6o7q

Robust Consensus for Nonlinear Multiagent Systems with Uncertainty and Disturbance

Zhiqiang Li, Chengjie Xu, Chen Liu, Haichuan Xu
2018 Mathematical Problems in Engineering  
This paper investigates robust consensus for nonlinear multiagent systems with uncertainty and disturbance.  ...  At first, the robust consensus condition is obtained and the convergency analysis is given by using Lyapunov stability theory and matrix theory.  ...  In this subsection, robust consensus for nonlinear multiagent systems is investigated in the case where 0 = 0 in Assumption 5. Theorem 11.  ... 
doi:10.1155/2018/8509306 fatcat:zvajc3rdgzebjpahaquj4gbmgm

Stochastic semistability with application to agreement problems over random networks

Jing Zhou, Qian Wang
2010 Proceedings of the 2010 American Control Conference  
In this paper, we consider the agreement problem of a group of agents with nonlinear stochastic dynamics and each agent applies a local (distributed) nonlinear consensus protocol over random networks.  ...  We have proposed the notion of almost sure semistability for nonlinear systems with a continuum of equilibrium solutions, and have derived a set of Lyapunov sufficient conditions for almost sure semistability  ...  Semistablity for nonlinear systems was developed in [4] , [5] , [6] and then applied to nonlinear consensus protocols over fixed networks in [10] .  ... 
doi:10.1109/acc.2010.5531065 fatcat:fw4gdvbwmzfkdbdjbfxtlv2mry

Stability analysis of a class of uncertain switched systems on time scale using Lyapunov functions

Fatima Zohra Taousser, Michael Defoort, Mohamed Djemai
2015 Nonlinear Analysis. Hybrid Systems  
Using the concept of common Lyapunov function, sufficient conditions are derived to guarantee the asymptotic stability of this class of systems on time scale with bounded graininess function.  ...  This paper deals with the stability analysis of a class of uncertain switched systems on nonuniform time domains.  ...  Acknowledgments This work has been supported by International Campus on Safety and Intermodality in Transportation, the European Community, the Délégation Régionale à la Recherche et à la Technologie,  ... 
doi:10.1016/j.nahs.2014.12.001 fatcat:qt7cmahuqjdfxbkpsqjn3cj4ei

About disconnected topologies and synchronization of homogeneous nonlinear agents over switching networks

G. Casadei, A. Isidori, L. Marconi
2017 International Journal of Robust and Nonlinear Control  
In this work a general class of nonlinear systems assumed to be "non-expansive" is considered, and strong joint connectivity of the graph is shown to be sufficient condition for consensus.  ...  In particular, the arguments presented here can be used to show that the control framework of [18] succeeds in achieving consensus between networked heterogeneous nonlinear systems even in presence of  ...  1, we introduce a common Lyapunov function proving consensus; • in the second part we study the behavior of the network for a fixed disconnected topology by means of Lyapunov arguments; • in the third  ... 
doi:10.1002/rnc.3910 fatcat:6j7x3c6nd5d2xcn2la3gp2vizu

2014 Index IEEE Transactions on Automatic Control Vol. 59

2014 IEEE Transactions on Automatic Control  
by Using a Lyapunov Function.  ...  ., +, TAC Feb. 2014 494-499 Global Finite-Time Stability Characterized Through a Local Notion of Homogeneity. 471-477 ISS-Lyapunov Functions for Discontinuous Discrete-Time Systems.  ... 
doi:10.1109/tac.2014.2382720 fatcat:jah5kqkafvejrd7xpvyikmi53e

Stability of switched nonlinear systems via extensions of LaSalle's invariance principle

JinHuan Wang, DaiZhan Cheng
2009 Science in China Series F Information Sciences  
This paper studies the extension of LaSalle's invariance principle for switched nonlinear systems.  ...  LaSalle's invariance principle, switched systems, weak common Lyapunov function, asymptotically stable  ...  In general, for switched nonlinear systems, it is not easy to obtain the global asymptotic stability result. Sometimes, we only need the local stability.  ... 
doi:10.1007/s11432-009-0006-z fatcat:vw3ilp75i5gsxpc7xqohphnboa

2008 Index IEEE Transactions on Automatic Control Vol. 53

2008 IEEE Transactions on Automatic Control  
The Author Index contains the primary entry for each item, listed under the first author's name.  ...  -that appeared in this periodical during 2008, and items from previous years that were commented upon or corrected in 2008.  ...  . , TAC Feb. 2008 441-442 Consensus algorithms On the Nonexistence of Quadratic Lyapunov Functions for Consensus Algorithms.  ... 
doi:10.1109/tac.2008.2010902 fatcat:5d76tgkjnvhohntuilcvl3jb3i
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