scholarly journals Second-Order Consensus for Multiagent Systems under Directed and Switching Topologies

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Lixin Gao ◽  
Jingjing Zhang ◽  
Wenhai Chen
Keyword(s):  
Function Method ◽  
Sufficient Conditions ◽  
Common Lyapunov Function ◽  
Special Cases ◽  
Lyapunov Function Method ◽  
Leader Following ◽  
The Common ◽  
Feedback Laws ◽  
Integrator Model ◽  
Double Integrator

We consider multiagent consensus problems in a decentralized fashion. The interconnection topology among the agents is switching and directed. The agent dynamics is expressed in the form of a double-integrator model. Two different cases are considered: one is the leader-following case and the other is the leaderless case. Based on graph theory and the common Lyapunov function method, some sufficient conditions are established for the consensus stability of the considered systems with the neighbor-based feedback laws in both leader-following case and leaderless case, respectively. As special cases, the consensus conditions for balanced and undirected interconnection topology cases can be established directly. Finally, two numerical examples are given to illustrate the obtained results.

Switching Control for a Class of Discrete-Time Switched Fuzzy Systems Based on LMI

2014 ◽  
Vol 945-949 ◽  
pp. 2543-2546
Author(s):  
Hong Yang ◽  
Huan Huan Lü ◽  
Le Zhang
Keyword(s):  
Discrete Time ◽  
Fuzzy Systems ◽  
Sufficient Conditions ◽  
Switching Control ◽  
Linear Matrix ◽  
Common Lyapunov Function ◽  
Lyapunov Function Method ◽  
The Common ◽  
The Stability ◽  
Stability Issues

Switching control and stability issues for discrete-time switched systems whose subsystems are all discrete-time fuzzy systems are studied and new results derived. Innovated representation models for switched fuzzy systems are proposed. The common Lyapunov function method has been adopted to study the stability of this class of switched fuzzy systems. Sufficient conditions for asymptotic stability are presented. The main conditions are given in form of linear matrix inequalities (LMIs), which are easily solvable. The elaborated illustrative examples and the respective simulation experiments demonstrate the effectiveness of the proposed method.

scholarly journals Distributed Attitude Consensus for Multiple Rigid Spacecraft under Jointly Connected Switching Topologies

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Long Ma ◽  
Shicheng Wang ◽  
Haibo Min ◽  
Shouyi Liao ◽  
Zhiguo Liu
Keyword(s):  
Function Method ◽  
Consensus Problem ◽  
Time Intervals ◽  
Common Lyapunov Function ◽  
Switching Topologies ◽  
First Case ◽  
Lyapunov Function Method ◽  
Communication Topology ◽  
Leader Following ◽  
Rigid Spacecraft

We study the distributed leader-following attitude consensus problem for multiple rigid spacecraft with a single leader under jointly connected switching topologies. Two cases are considered, where the first case is with a static leader and the second case is with a dynamic leader. By constructing an auxiliary vector and a distributed observer for each follower spacecraft, the controllers are designed to drive all the attitudes of the follower spacecraft to the leader’s, respectively, for both of the two cases, though there are some time intervals in which the communication topology is not connected. The whole system is proved to be stable by using common Lyapunov function method. Finally, the theoretical result is illustrated by numerical simulations.

scholarly journals Leader-Following Consensus of Linear Multiagent Systems with State Observer under Switching Topologies

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Lixin Gao ◽  
Xinjian Zhu ◽  
Wenhai Chen ◽  
Hui Zhang
Keyword(s):  
Multiagent Systems ◽  
Function Method ◽  
Tracking Error ◽  
Protocol Design ◽  
Design Technique ◽  
Special Cases ◽  
Lyapunov Function Method ◽  
Communication Topology ◽  
Leader Following ◽  
Parameter Dependent

The leader-following consensus problem of higher order multiagent systems is considered. The dynamics of each agent are given in general form of linear system, and the communication topology among the agents is assumed to be directed and switching. To track the leader, two kinds of distributed observer-based consensus protocols are proposed for each following agent, whose distributed observers are used to estimate the leader’s state and tracking error based on the relative outputs of the neighboring agents, respectively. Some sufficient consensus conditions are established by using parameter-dependent Lyapunov function method under a class of directed interaction topologies. As special cases, the consensus conditions for balanced and undirected interconnection topology cases can be obtained directly. The protocol design technique is based on algebraic graph theory, Riccati equation, and Sylvester equation. Finally, a simulation example is given to illustrate our obtained result.

scholarly journals On the General Consensus Protocol in Multiagent Networks with Double-Integrator Dynamics and Coupling Time Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Tao Dong ◽  
Xiaofeng Liao
Keyword(s):  
Time Delay ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Consensus Algorithm ◽  
Directed Network ◽  
Consensus Protocol ◽  
Special Cases ◽  
Coupling Time ◽  
Almost All ◽  
Double Integrator

This paper considers the problem of the convergence of the consensus algorithm for multiple agents in a directed network where each agent is governed by double-integrator dynamics and coupling time delay. The advantage of this protocol is that almost all the existing linear local interaction consensus protocols can be considered as special cases of the present paper. By combining algebraic graph theory and matrix theory and studying the distribution of the eigenvalues of the associated characteristic equation, some necessary and sufficient conditions are derived for reaching the second-order consensus. Finally, an illustrative example is also given to support the theoretical results.

scholarly journals Global Attractivity of a Periodic DelayedN-Species Model of Facultative Mutualism

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Ahmadjan Muhammadhaji ◽  
Zhidong Teng
Keyword(s):  
Lyapunov Function ◽  
Periodic Solutions ◽  
Function Method ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Positive Periodic Solutions ◽  
Facultative Mutualism ◽  
Lyapunov Function Method

Two classes of periodicN-species Lotka-Volterra facultative mutualism systems with distributed delays are discussed. Based on the continuation theorem of the coincidence degree theory developed by Gaines and Mawhin and the Lyapunov function method, some new sufficient conditions on the existence and global attractivity of positive periodic solutions are established.

scholarly journals Exponential Synchronization of Stochastic Complex Dynamical Networks with Impulsive Perturbations and Markovian Switching

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Wuneng Zhou ◽  
Anding Dai ◽  
Dongbing Tong ◽  
Jun Yang
Keyword(s):  
Stochastic Analysis ◽  
Function Method ◽  
Transition Probability ◽  
Sufficient Conditions ◽  
Exponential Synchronization ◽  
Markovian Switching ◽  
Complex Dynamical Networks ◽  
Dynamical Networks ◽  
Synchronization Problem ◽  
Lyapunov Function Method

This paper investigates the exponential synchronization problem of stochastic complex dynamical networks with impulsive perturbation and Markovian switching. The complex dynamical networks consist ofκmodes, and the networks switch from one mode to another according to a Markovian chain with known transition probability. Based on the Lyapunov function method and stochastic analysis, by employingM-matrix approach, some sufficient conditions are presented to ensure the exponential synchronization of stochastic complex dynamical networks with impulsive perturbation and Markovian switching, and the upper bound of impulsive gain is evaluated. At the end of this paper, two numerical examples are included to show the effectiveness of our results.

Maximal and Minimal Ranks of the Common Solution of Some Linear Matrix Equations over an Arbitrary Division Ring with Applications

2009 ◽  
Vol 16 (02) ◽  
pp. 293-308 ◽  
Author(s):  
Qingwen Wang ◽  
Guangjing Song ◽  
Xin Liu
Keyword(s):  
Division Ring ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Linear Matrix ◽  
Matrix Equations ◽  
Common Solution ◽  
Special Cases ◽  
The Common ◽  
Necessary And Sufficient ◽  
Linear Matrix Equations

We establish the formulas of the maximal and minimal ranks of the common solution of certain linear matrix equations A1X = C1, XB2 = C2, A3XB3 = C3 and A4XB4 = C4 over an arbitrary division ring. Corresponding results in some special cases are given. As an application, necessary and sufficient conditions for the invariance of the rank of the common solution mentioned above are presented. Some previously known results can be regarded as special cases of our results.

Distributed H∞ Control for Leader-Following Coordination with Switching Topology

2011 ◽  
Vol 135-136 ◽  
pp. 455-463
Author(s):  
Yan Ping Luo ◽  
Li Xin Gao
Keyword(s):  
Control Problem ◽  
External Disturbance ◽  
Switching Topology ◽  
Consensus Control ◽  
Common Lyapunov Function ◽  
Control Laws ◽  
Leader Following ◽  
Multi Agent ◽  
Feedback Laws ◽  
Parameter Dependent

In this paper, we consider multi-agent H∞consensus control problems with external disturbance under the undirected switching topologies. The agent dynamics is expressed in the form of a second-order model and the control laws are neighbor-based feedback laws. By using the model transformation, the multi-agent H∞consensus control problem is converted into H∞ control problem for a switching linear system with special structure. A sufficient condition is established under which all agents can reach consensus with the desired H∞performance in switching topology case by constructing a parameter-dependent common Lyapunov function. Moreover, we give an explicit estimation expression to estimate H∞ performance index. Finally, a numerical example is provided to illustrate the effectiveness of our results.

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