scholarly journals State Consensus Analysis and Design for High-Order Discrete-Time Linear Multiagent Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Yanrong Ge ◽  
Yangzhou Chen ◽  
Yaxiao Zhang ◽  
Zhonghe He
Keyword(s):  
Multiagent Systems ◽  
Discrete Time ◽  
The State ◽  
Feedback Gain ◽  
Consensus Problem ◽  
Consensus Protocol ◽  
Consensus Function ◽  
Consensus Analysis ◽  
Analysis And Design ◽  
Time Linear

The paper deals with the state consensus problem of high-order discrete-time linear multiagent systems (DLMASs) with fixed information topologies. We consider three aspects of the consensus analysis and design problem: (1) the convergence criteria of global state consensus, (2) the calculation of the state consensus function, and (3) the determination of the weighted matrix and the feedback gain matrix in the consensus protocol. We solve the consensus problem by proposing a linear transformation to translate it into a partial stability problem. Based on the approach, we obtain necessary and sufficient criteria in terms of Schur stability of matrices and present an analytical expression of the state consensus function. We also propose a design process to determine the feedback gain matrix in the consensus protocol. Finally, we extend the state consensus to the formation control. The results are explained by several numerical examples.

Distributed event-triggered consensus protocols for discrete-time multiagent systems

2021 ◽  
Author(s):  
Bilal J Karaki ◽  
Magdi S Mahmoud
Keyword(s):  
Multiagent Systems ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Control Law ◽  
Theory Approach ◽  
Consensus Protocol ◽  
Leader Following ◽  
And Control ◽  
Time Linear ◽  
Event Triggered

Abstract This paper focuses on leader-following and leaderless consensus problems of discrete-time multiagent systems. A distributed observer-based consensus protocol is proposed to investigate the consensus problem for multiagent systems of general discrete-time linear dynamics. By means of the observer, the distributed control law of each agent is designed using local information to guarantee consensus, and the corresponding sufficient conditions are obtained by exploiting graph and control theory approach. A modified distributed event-triggered consensus protocol is designed to reduce communication congestion. Detailed analysis of the leaderless and the leader-following consensus is presented for both observer-based and full-information protocols. Finally, two simulation examples are provided to demonstrate the effectiveness and capabilities of the established theories.

New Conditions and Numerical Checking Method for the Practical Stability of Fractional Order Positive Discrete-Time Linear Systems

2019 ◽  
Vol 20 (3-4) ◽  
pp. 315-323
Author(s):  
Hongli Yang ◽  
Yuexiao Jia
Keyword(s):  
Fractional Order ◽  
Discrete Time ◽  
The State ◽  
Practical Stability ◽  
Space Systems ◽  
State Matrix ◽  
Numerical Examples ◽  
State Space Systems ◽  
Linear State ◽  
Time Linear

AbstractPractical stability of a fractional order discrete-time linear state-space systems was put up in recent years. It is usually checked by the eigenvalues of the state matrix, some methods have been given during these years. But if the size of the state matrix is large, the computations of eigenvalues can be very onerous. In this paper, some new conditions on practical stability for positive fractional discrete-time linear system are presented. Numerically checking method of practical stability is presented based on the new conditions given in this paper. It is illustrated by the numerical examples that our checking method is effective and true. Compared to the now existing methods, numerically checking method is an attractive method because it’s easily implemented.

scholarly journals Bipartite Consensus of Heterogeneous Multiagent Systems Based on Distributed Event-Triggered Control

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-14 ◽  
Author(s):  
Xiaoyu Wang ◽  
Kaien Liu ◽  
Zhijian Ji ◽  
Shitao Han
Keyword(s):  
Multiagent Systems ◽  
Sufficient Conditions ◽  
Input Delay ◽  
Consensus Problem ◽  
Consensus Protocol ◽  
Control Scheme ◽  
Event Triggering ◽  
Bipartite Consensus ◽  
Theoretical Results ◽  
Event Triggered

In this paper, the bipartite consensus problem of heterogeneous multiagent systems composed of first-order and second-order agents is considered by utilizing the event-triggered control scheme. Under structurally balanced directed topology, event-triggered bipartite consensus protocol is put forward, and event-triggering functions consisting of measurement error and threshold are designed. To exclude Zeno behavior, an exponential function is introduced in the threshold. The bipartite consensus problem is transformed into the corresponding stability problem by means of gauge transformation and model transformation. By virtue of Lyapunov method, sufficient conditions for systems without input delay are obtained to guarantee bipartite consensus. Furthermore, for the case with input delay, sufficient conditions which include an admissible upper bound of the delay are obtained to guarantee bipartite consensus. Finally, numerical simulations are provided to illustrate the effectiveness of the obtained theoretical results.

Analysis and design for discrete-time linear systems subject to actuator saturation

2002 ◽  
Vol 45 (2) ◽  
pp. 97-112 ◽  
Author(s):  
Tingshu Hu ◽  
Zongli Lin ◽  
Ben M. Chen
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Actuator Saturation ◽  
Analysis And Design ◽  
Time Linear

scholarly journals SINGULAR FRACTIONAL CONTINUOUS-TIME AND DISCRETE-TIME LINEAR SYSTEMS

2013 ◽  
Vol 7 (1) ◽  
pp. 26-33 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
State Equation ◽  
Electrical Circuit ◽  
The State ◽  
Continuous Time Systems ◽  
Definition Of ◽  
Time Systems ◽  
Time Linear

Abstract New classes of singular fractional continuous-time and discrete-time linear systems are introduced. Electrical circuits are example of singular fractional continuous-time systems. Using the Caputo definition of the fractional derivative, the Weierstrass regular pencil decomposition and Laplace transformation the solution to the state equation of singular fractional linear systems is derived. It is shown that every electrical circuit is a singular fractional systems if it contains at least one mesh consisting of branches with only ideal supercondensators and voltage sources or at least one node with branches with supercoils. Using the Weierstrass regular pencil decomposition the solution to the state equation of singular fractional discrete-time linear systems is derived. The considerations are illustrated by numerical examples.

scholarly journals Descriptor fractional linear systems with regular pencils

2013 ◽  
Vol 23 (2) ◽  
pp. 309-315 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Laplace Transform ◽  
Linear Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
The State ◽  
Transition Matrices ◽  
State Equations ◽  
Numerical Examples ◽  
The Laplace Transform ◽  
Time Linear

Methods for finding solutions of the state equations of descriptor fractional discrete-time and continuous-time linear systems with regular pencils are proposed. The derivation of the solution formulas is based on the application of the Z transform, the Laplace transform and the convolution theorems. Procedures for computation of the transition matrices are proposed. The efficiency of the proposed methods is demonstrated on simple numerical examples.

KETEROBSERVASIAN SISTEM LINIER DISKRIT

2015 ◽  
Vol 4 (1) ◽  
pp. 108
Author(s):  
Midian Manurung
Keyword(s):  
Linear System ◽  
Discrete Time ◽  
State Vector ◽  
The State ◽  
Input Vector ◽  
Linear Control ◽  
Time Interval ◽  
Initial State ◽  
Time Invariant ◽  
Time Linear

Given the following discrete time-invariant linear control systems:where x 2 Rnx(t + 1) = Ax(t) + Bu(t);y(t) = Cx(t);is the state vector, u 2 Rmis an input vector, y 2 Rris dened as anoutput, A 2 Rnn, B 2 Rnm, and t 2 Zis dened as time. Linear system is said to beobservable on the nite time interval [t0; t+f] if any initial state xis uniquely determinedby the output y(t) over the same time interval. In order to examine the observabilityof the system, we will use a criteria, that is by determining the observability Gramianmatrix of the system is nonsingular and rank of the observability matrix for the systemis n.

Set-Membership Filtering-Based Leader–Follower Synchronization of Discrete-Time Linear Multi-Agent Systems

2021 ◽  
Vol 143 (6) ◽  
Author(s):  
Diganta Bhattacharjee ◽  
Kamesh Subbarao
Keyword(s):  
Discrete Time ◽  
The State ◽  
Multi Agent Systems ◽  
State Estimator ◽  
Agent Systems ◽  
Set Membership ◽  
Multi Agent ◽  
Bounded Input ◽  
Time Linear ◽  
Synchronization Protocol

Abstract In this paper, a set-membership filtering-based leader–follower synchronization protocol for discrete-time linear multi-agent systems is proposed, wherein the aim is to make the agents synchronize with a leader. The agents, governed by identical high-order discrete-time linear dynamics, are subject to unknown-but-bounded input disturbances. In terms of its own state information, each agent only has access to measured outputs that are corrupted with unknown-but-bounded output disturbances. Also, the initial states of the agents are unknown. To deal with all these unknowns (or uncertainties), a set-membership filter (or state estimator), having the “correction-prediction” form of a standard Kalman filter, is formulated. We consider each agent to be equipped with this filter that estimates the state of the agent and consider the agents to be able to share the state estimate information with the neighbors locally. The corrected state estimates of the agents are utilized in the local control law design for synchronization. Under appropriate conditions, the global disagreement error between the agents and the leader is shown to be bounded. An upper bound on the norm of the global disagreement error is calculated and shown to be monotonically decreasing. Finally, a simulation example is included to illustrate the effectiveness of the proposed leader–follower synchronization protocol.

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