On the Boundary Value of the Time-Delay and the Asymptotic Behavior of a Continuous First-Order Consensus Protocol-Reference-Cited by-同舟云学术

On the Boundary Value of the Time-Delay and the Asymptotic Behavior of a Continuous First-Order Consensus Protocol

Published:2024-06 Issue:6 Volume:85 Page:610-620
ISSN:0005-1179
Container-title:Automation and Remote Control
language:
Short-container-title:ARC

Author:

Agaev R. P., ,Khomutov D. K.,

Abstract

Coordination in multiagent systems with information influences is studied. In particular, a model of multiagent system in which information is transmitted with a constant delay for all agents is studied. Using the Nyquist criterion applied by Tsypkin for systems with delayed feedback, a formula is obtained for the boundary value of time-delay which is included as a parameter in the system of differential equations with an asymmetric constant Laplacian matrix. The condition of independence of stability from time-delay is founded. The results obtained generalize some previously results and can be applied in coordination analysis in a multiagent systems with complex protocol.

Publisher

The Russian Academy of Sciences

Reference34 articles.

1. 1. Elsgolts, L.E. and Norkin, S.B., Vvedenie v teoriyu differentsial'nykh uravnenii s otklonyayushchimsya argumentom (Introduction to the theory of differential equations with divergent argument), Moscow: Nauka, 1971.

2. 2. Chebotarev, N.G. and Meiman, N.N., The Routh-Hurwitz problem for polynomials and entire functions, Trudy Matematicheskogo Instituta imeni V.A. Steklova, 1949, vol. 26, pp. 3-331.

3. 3. Pontryagin, L.S., On the zeros of some elementary transcendental functions [Russian] Izv. Akad. Nauk SSR, Ser. Mat., 1942, vol .6, no. 3, pp. 115-134.

4. 4. Bellman, R. and Cooke, K., Differentsial'no-raznostnye uravneniya (Differential-difference equations), Moscow: Mir, 1966.

5. 5. Kolmanovskii, V. and Myshkis, A., Applied Theory of Functional Differential Equations, Dordrecht: Kluwer Academic Publishers, 1992.