Consensus in hierarchical multi-agent dynamical systems with low-rank interconnections: Analysis of stability and convergence rates

2009 ◽  
Author(s):  
Shinji Hara ◽  
Hikaru Shimizu ◽  
Tae-Hyoung Kim
Keyword(s):  
Dynamical Systems ◽  
Convergence Rates ◽  
Low Rank ◽  
Stability And Convergence ◽  
Multi Agent ◽  
Analysis Of Stability

Monotone Semiflows Generated by Neutral Functional Differential Equations With Application to Compartmental Systems

1991 ◽  
Vol 43 (5) ◽  
pp. 1098-1120 ◽  
Author(s):  
Jianhong Wu ◽  
H. I. Freedman
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Stability And Convergence ◽  
Strong Monotonicity ◽  
Neutral Functional Differential Equations ◽  
Neutral Equations ◽  
Functional Differential ◽  
Monotone Dynamical Systems

AbstractThis paper is devoted to the machinery necessary to apply the general theory of monotone dynamical systems to neutral functional differential equations. We introduce an ordering structure for the phase space, investigate its compatibility with the usual uniform convergence topology, and develop several sufficient conditions of strong monotonicity of the solution semiflows to neutral equations. By applying some general results due to Hirsch and Matano for monotone dynamical systems to neutral equations, we establish several (generic) convergence results and an equivalence theorem of the order stability and convergence of precompact orbits. These results are applied to show that each orbit of a closed biological compartmental system is convergent to a single equilibrium.

scholarly journals A homogeneity property of discrete‐time systems: Stability and convergence rates

2019 ◽  
Vol 29 (8) ◽  
pp. 2406-2421 ◽  
Author(s):  
Tonametl Sanchez ◽  
Denis Efimov ◽  
Andrey Polyakov ◽  
Jaime A. Moreno ◽  
Wilfrid Perruquetti
Keyword(s):  
Discrete Time ◽  
Convergence Rates ◽  
Stability And Convergence ◽  
Discrete Time Systems ◽  
Homogeneity Property ◽  
Time Systems

scholarly journals Robust Consensus for a Class of Uncertain Multi-Agent Dynamical Systems

2013 ◽  
Vol 9 (1) ◽  
pp. 306-312 ◽  
Author(s):  
Dongkun Han ◽  
Graziano Chesi ◽  
Yeung Sam Hung
Keyword(s):  
Dynamical Systems ◽  
Multi Agent ◽  
Robust Consensus

Flocking of multi-agent dynamical systems with intermittent nonlinear velocity measurements

2011 ◽  
Vol 22 (16) ◽  
pp. 1790-1805 ◽  
Author(s):  
Guanghui Wen ◽  
Zhisheng Duan ◽  
Zhongkui Li ◽  
Guanrong Chen
Keyword(s):  
Dynamical Systems ◽  
Velocity Measurements ◽  
Multi Agent ◽  
Nonlinear Velocity

An Efficient Numerical Simulation for Solving Dynamical Systems With Uncertainty

2017 ◽  
Vol 12 (5) ◽  
Author(s):  
Ali Ahmadian ◽  
Soheil Salahshour ◽  
Chee Seng Chan ◽  
Dumitur Baleanu
Keyword(s):  
Dynamical Systems ◽  
Stability And Convergence ◽  
Uncertain Parameters ◽  
Crucial Issue ◽  
Computational Costs ◽  
First Order ◽  
Wide Range ◽  
Linear And Nonlinear ◽  
The Stability ◽  
Fuzzy Dynamical Systems

In a wide range of real-world physical and dynamical systems, precise defining of the uncertain parameters in their mathematical models is a crucial issue. It is well known that the usage of fuzzy differential equations (FDEs) is a way to exhibit these possibilistic uncertainties. In this research, a fast and accurate type of Runge–Kutta (RK) methods is generalized that are for solving first-order fuzzy dynamical systems. An interesting feature of the structure of this technique is that the data from previous steps are exploited that reduce substantially the computational costs. The major novelty of this research is that we provide the conditions of the stability and convergence of the method in the fuzzy area, which significantly completes the previous findings in the literature. The experimental results demonstrate the robustness of our technique by solving linear and nonlinear uncertain dynamical systems.

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