scholarly journals Group Consensus of Heterogeneous Multiagent Systems with Time Delay

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Weixun Li ◽  
Liqiong Zhang
Keyword(s):  
Time Delay ◽  
Multiagent Systems ◽  
Control Algorithm ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Group Consensus ◽  
Communication Time ◽  
Theoretical Results

In this paper, a neighbour-based control algorithm of group consensus is designed for a class of hybrid-based heterogeneous multiagent systems with communication time delay. We consider the statics leaders and active leaders, respectively. The original systems are transformed into new error systems by transformation. On the basis of the systems, applying Lyapunov stability theory and adopting the linear matrix inequality method, sufficient conditions which guarantee the heterogeneous multiagent systems stability are obtained. To illustrate the validity of theoretical results, some numerical simulations are given at the end of the paper.

scholarly journals H∞Consensus for Multiagent Systems with Heterogeneous Time-Varying Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Beibei Wang ◽  
Yuangong Sun
Keyword(s):  
Multiagent Systems ◽  
Multiagent System ◽  
Sufficient Conditions ◽  
Order System ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Reduced Order ◽  
Heterogeneous Delays ◽  
Theoretical Results

We apply the linear matrix inequality method to consensus andH∞consensus problems of the single integrator multiagent system with heterogeneous delays in directed networks. To overcome the difficulty caused by heterogeneous time-varying delays, we rewrite the multiagent system into a partially reduced-order system and an integral system. As a result, a particular Lyapunov function is constructed to derive sufficient conditions for consensus of multiagent systems with fixed (switched) topologies. We also apply this method to theH∞consensus of multiagent systems with disturbances and heterogeneous delays. Numerical examples are given to illustrate the theoretical results.

scholarly journals Exponential Stability of Stochastic Differential Equation with Mixed Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Wenli Zhu ◽  
Jiexiang Huang ◽  
Xinfeng Ruan ◽  
Zhao Zhao
Keyword(s):  
Differential Equation ◽  
Time Delay ◽  
Stochastic Differential Equation ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Martingale Inequality ◽  
Mixed Delay ◽  
Exponentially Stable ◽  
Theoretical Results

This paper focuses on a class of stochastic differential equations with mixed delay based on Lyapunov stability theory, Itô formula, stochastic analysis, and inequality technique. A sufficient condition for existence and uniqueness of the adapted solution to such systems is established by employing fixed point theorem. Some sufficient conditions of exponential stability and corollaries for such systems are obtained by using Lyapunov function. By utilizing Doob’s martingale inequality and Borel-Cantelli lemma, it is shown that the exponentially stable in the mean square of such systems implies the almost surely exponentially stable. In particular, our theoretical results show that if stochastic differential equation is exponentially stable and the time delay is sufficiently small, then the corresponding stochastic differential equation with mixed delay will remain exponentially stable. Moreover, time delay upper limit is solved by using our theoretical results when the system is exponentially stable, and they are more easily verified and applied in practice.

scholarly journals Exponential Stability of Stochastic Nonlinear Dynamical Price System with Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Wenli Zhu ◽  
Xinfeng Ruan ◽  
Ye Qin ◽  
Jie Zhuang
Keyword(s):  
Time Delay ◽  
Exponential Stability ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Price System ◽  
Nonlinear Dynamical ◽  
System With Delay ◽  
Exponentially Stable ◽  
Theoretical Results

Based on Lyapunov stability theory, Itô formula, stochastic analysis, and matrix theory, we study the exponential stability of the stochastic nonlinear dynamical price system. Using Taylor's theorem, the stochastic nonlinear system with delay is reduced to ann-dimensional semilinear stochastic differential equation with delay. Some sufficient conditions of exponential stability and corollaries for such price system are established by virtue of Lyapunov function. The time delay upper limit is solved by using our theoretical results when the system is exponentially stable. Our theoretical results show that if the classical price Rayleigh equation is exponentially stable, so is its perturbed system with delay provided that both the time delay and the intensity of perturbations are small enough. Two examples are presented to illustrate our results.

scholarly journals Consensus of Multiagent Systems with Directed Topology and Communication Time Delay Bases on the Laplace Transform

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Bo Liu ◽  
Li Wang ◽  
Dehui Sun ◽  
Xinmao Zhu
Keyword(s):  
Time Delay ◽  
Laplace Transform ◽  
Multiagent Systems ◽  
Consensus Problem ◽  
Directed Topology ◽  
Communication Time ◽  
The Laplace Transform ◽  
Initial States ◽  
Directed Topologies ◽  
Theoretical Results

This paper investigates the consensus problem of multiagent systems with directed topologies. Different from the literatures, a new method, the Laplace transform, to study the consensus of multiagent systems with directed topology and communication time delay is proposed. The accurate state of the consensus center and the upper bound of the communication delay to make the agents reach consensus are given. It is proved that all the agents could aggregate and eventually form a cohesive cluster in finite time under certain conditions, and the consensus center is only determined by the initial states and the communication configuration among the agents. Finally, simulations are given to illustrate the theoretical results.

scholarly journals Couple-Group Consensus: A Class of Delayed Heterogeneous Multiagent Systems in Competitive Networks

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Lianghao Ji ◽  
Yue Zhang ◽  
Yiliu Jiang
Keyword(s):  
Multiagent Systems ◽  
Time Delays ◽  
Heterogeneous Systems ◽  
Velocity Estimation ◽  
Communication Delays ◽  
Group Consensus ◽  
Distributed Coordination ◽  
First Order ◽  
Communication Time ◽  
Theoretical Results

This paper discusses the couple-group consensus issues of a class of heterogeneous multiagent systems containing first-order and second-order dynamic agents under the influence of both input and communication delays. In distinction to the existing works, a novel distributed coordination control protocol is proposed which is not only on the foundation of the competitive interaction between the agents but also has no virtual velocity estimation in the first-order dynamics. Furthermore, without the restrictive assumptions existing commonly in the related works, several sufficient algebraic criteria are established for the heterogeneous systems to realize couple-group consensus asymptotically. The obtained conclusions show that the achievement of the systems’ couple-group consensus intimately relates to the coupling weights between the agents, the systems control parameters, and the input time delays of the agents, while communication time delays between the agents are irrelevant to it. Finally, several simulations are illustrated to verify the effectiveness of the obtained theoretical results.

scholarly journals Consensus Conditions for a Class of Fractional-Order Nonlinear Multiagent Systems with Constant and Time-Varying Time Delays

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Xiaorong Zhang ◽  
Min Shi
Keyword(s):  
Time Delay ◽  
Multiagent Systems ◽  
Fractional Order ◽  
Time Delays ◽  
Constant Time Delay ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Varying Delay ◽  
Theoretical Results

The consensus problem for a class of fractional-order nonlinear multiagent systems with a distributed protocol containing input time delay is investigated in this paper. Consider both cases of constant time delay and time-varying delay, the delay-independent consensus conditions are obtained to achieve the consensus of the systems, respectively, by adopting the linear matrix inequality (LMI) methods and stability theory of fractional-order systems. As illustrated by the numerical examples, the proposed theoretical results work well and accurately.

scholarly journals Passivity analysis of multiple time-varying time delayed complex variable neural networks in finite-time

2021 ◽  
Vol 8 (4) ◽  
pp. 842-854
Author(s):  
N. Jayanthi ◽  
◽  
R. Santhakumari ◽  
Keyword(s):  
Neural Networks ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Multiple Time ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Complex Valued ◽  
Theoretical Results

In this article, we investigate the problem of finite-time passivity for the complex-valued neural networks (CVNNs) with multiple time-varying delays. To begin, many definitions relevant to the finite-time passivity of CVNNs are provided; then the suitable control inputs are designed to guarantee the class of CVNNs are finite-time passive. In the meantime, some sufficient conditions of linear matrix inequalities (LMIs) are derived by using inequalities techniques and Lyapunov stability theory. Finally, a numerical example is presented to illustrate the usefulness of the theoretical results.

The Asymptotical Stability Analysis for Switched Descriptor Systems

2010 ◽  
Vol 29-32 ◽  
pp. 2150-2156 ◽  
Author(s):  
Wei Liu ◽  
Zi Yun Lu
Keyword(s):  
Numerical Simulation ◽  
Stability Analysis ◽  
Time Delay ◽  
Lyapunov Stability Theory ◽  
Asymptotical Stability ◽  
Descriptor Systems ◽  
Linear Matrix ◽  
Control Law ◽  
Matrix Inequality ◽  
Vector Matrix

This paper is concerned with the asymptotical stability analysis for a class of switched uncertain descriptor systems with time-delay. The robustly asymptotical stability of this system is proven by making use of the generalized Lyapunov Stability theory, linear matrix inequality (LMI) tools and multiple Lyapunov function techniques. The conservation of result is greatly reduced by means of introducing the optimal weight matrix and avoiding vector matrix inequality in deducing procedure, in which there is no need of transformation and hypothesis for descriptor systems. The designed control law could surely make switched Descriptor Systems quickly approach the balanceable point. Experimentally, one numerical simulation verifies the effectiveness of this method.

Resilient anti-disturbance H∞ control for turbofan systems

2020 ◽  
Vol 42 (14) ◽  
pp. 2686-2697
Author(s):  
Yankai Li ◽  
Mou Chen ◽  
Tao Li ◽  
Huijiao Wang ◽  
Yu Kang
Keyword(s):  
Disturbance Observer ◽  
Closed Loop ◽  
Control Method ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Control Technique ◽  
Linear Matrix ◽  
Asymptotically Stable ◽  
Matrix Inequality ◽  
Closed Loop Systems

The problem of [Formula: see text] control is investigated for turbofan systems with uncertain parameters and multiple disturbances in this paper. Some disturbances with partly known information are described via an external system, and other disturbances are assumed to be [Formula: see text] norm bounded. According to the disturbance-observer-based-control (DOBC) method and resilient [Formula: see text] control technique, a robust resilient controller is designed to reject and attenuate the influence of these disturbances, and guarantees that closed-loop systems are asymptotically stable with [Formula: see text] performance. Some solvable sufficient conditions are obtained based on the linear matrix inequality (LMI) technique and Lyapunov stability theory. Finally, a simulation is presented to show the robustness and effectiveness of the developed resilient anti-disturbance [Formula: see text] control method.

scholarly journals RobustH∞Control for Discrete-Time Stochastic Interval System with Time Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Shengchun Yu ◽  
Guici Chen ◽  
Yi Shen
Keyword(s):  
Time Delay ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Delay System ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Time Delay System ◽  
Interval System ◽  
Uncertain Time ◽  
System With Time Delay

The robustH∞control problem for discrete-time stochastic interval system (DTSIS) with time delay is investigated in this paper. The stochastic interval system is equivalently transformed into a kind of stochastic uncertain time-delay system firstly. By constructing the appropriate Lyapunov-Krasovskii functional, the sufficient conditions for the existence of the robustH∞controller for DTSIS are obtained in terms of linear matrix inequality (LMI) form, and the robustH∞controller is designed. Finally, a numerical example with simulation is given to show the effectiveness and correctness of the designed robustH∞controller.

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