References
- ALDOUS, D. (1991) Applications of random walks on finite graphs. IMS Lecture Notes-Monograph Series 18, 12–26. DOI: https://www.jstor.org/stable/4355644
- BONDY, J. A. and MURTY, U. S. R. (2008) Graph Theory. Springer-Verlag, London.
- CHEN, F. and REN, W. (2019) On the control of multi-agent systems: A survey. Foundations and Trends in Systems and Control 6 (4), 339–499. DOI: https://doi.org/10.1561/2600000019
- COPPERSMITH, D., DOYLE, P., RAGHAVAN, P. and SNIR, M. (1993) Random walks on weighted graphs and applications to on-line algorithms. Journal of the ACM 40 (3), 421–453. DOI: https://doi.org/10.1145/174130.17413110.1145/174130.174131
- DEFOORT, M., POLYAKOV A., DEMESURE, G., DJEMAI, M. and VELUVOLU, K. (2015) Leader–follower fixed-time consensus for multi-agent systems with unknown non-linear inherent dynamics. IET Control Theory & Applications 9 (14), 2165–2170. DOI: https://doi.org/10.1049/iet-cta.2014.1301
- FRIEDBERG, S. H., INSEL, A. J. and SPENCE, L. W. (1989) Linear Algebra. Prentice Hall, New Jersey.
- GENG, H., WU, H., MIAO, J., HOU, S. and CHEN, Z. (2022) Consensus of heterogeneous multi-agent systems under directed topology. IEEE Access 10, 5936–5943. DOI: https://doi.org/10.1109/ACCESS.2022.3142539
- GREGUŠ, M. (1987) Third Order Linear Differential Equations. D. Reidel Publishing Company, Dordrecht.
- GUAN, Y., JI, Z., ZHANG, L. and WANG, L. (2016) Controllability of heterogeneous multi-agent systems under directed and weighted topology. International Journal of Control 89 (5), 1009–1024. DOI: https://doi.org/10.1080/00207179.2015.1110756
- JAYARAMAN, G., PADMANABHAN, N. and MEHROTRA, R. (1986) Entry flow into a circular tube of slowly varying cross section. Fluid Dynamics Research 1 (2), 131–144. DOI: https://doi.org/10.1016/0169-5983(86)90013-4
- KURRAS, S. (2016) Variants of the Graph Laplacian with Applications in Machine Learning. Ph.D. dissertation. Universit¨at Hamburg, Hamburg.
- LELEUX, P., COURTAIN, S., FRANCOISSE, K. and SAERENS, M. (2022) Design of biased random walks on a graph with application to collaborative recommendation. Physica A: Statistical Mechanics and its Applications 590, 126752. DOI: https://doi.org/10.1016/j.physa.2021.126752
- LIU, J., AN, B. and WU, H. (2018) Consensus of third-order multi-agent systems with communication delay. 2018 Chinese Control And Decision Conference, 1428–1432. DOI: https://doi.org/10.1109/CCDC.2018.8407351
- LIU, Y.-Y. and BARABÁSI, A.-L. (2016) Control principles of complex systems. Reviews of Modern Physics 88 (3), 035006. DOI: https://doi.org/10.1103/RevModPhys.88.035006
- LIU, B., CHU, T., WANG, L. and XIE, G. (2008) Controllability of a leader–follower dynamic network with switching topology. IEEE Transactions on Automatic Control 53 (4), 1009–1013. DOI: https://doi.org/10.1109/TAC.2008.919548
- LIU, K., XIE, G. and WANG, L. (2012) Consensus for multi-agent systems under double integrator dynamics with time-varying communication delays. International Journal of Robust and Nonlinear Control 22 (17), 1881–1898. DOI: https://doi.org/10.1002/rnc.1792
- LOZANO, R., SPONG, M. W., GUERRERO, J. A. and CHOPRA, N. (2008) Controllability and observability of leader-based multi-agent systems. 47th IEEE Conference on Decision and Control, 3713–3718. DOI: https://doi.org/10.1109/CDC.2008.4739071
- MESBAHI, M. and EGERSTEDT, M. (2010) Graph Theoretic Methods in Multiagent Networks. Princeton University Press, Princeton.
- MUNI, V. S., RAFEEK, K. V. M., ATHIRA, V. S. and REDDY, G. J. (2023) Controllability of consensus of multi-agent networks over heterogeneous dynamics. Results in Control and Optimization 12, 100272. DOI: https://doi.org/10.1016/j.rico.2023.100272
- MUNI, V. S., RAFEEK, K. V. M., REDDY, G. J. and GEORGE, R. K. (2022) On the selection of leaders for the controllability of multi-agent networks. Bulletin of the Iranian Mathematical Society 48 (6), 3141–3183. DOI: https://doi.org/10.1007/s41980-022-00683-2
- PADHI, S. and PATI, S. (2014) Theory of Third-Order Differential Equations. Springer, New Delhi.
- REN, W. (2007) Consensus strategies for cooperative control of vehicle formations. IET Control Theory & Applications 1 (2), 505–512. DOI: https://doi.org/10.1049/iet-cta:20050401
- REN, W. and BEARD, R. W. (2005) Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Transactions on Automatic Control 50 (5), 655–661. DOI: https://doi.org/10.1109/TAC.2005.846556
- REYNOLDS, D. W. (1989) Bifurcation of harmonic solutions of an integrodifferential equation modelling resonant sloshing. SIAM Journal of Applied Mathematics 49 (2), 362–372. DOI: https://doi.org/10.1137/0149022
- SABER, R. O. and MURRAY, R. M. (2004) Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on Automatic Control 49 (9), 1520–1533. DOI: https://doi.org/10.1109/TAC.2004.834113
- TANNER, H. G. (2004) On the controllability of nearest neighbour interconnections. 43rd IEEE Conference on Decision and Control, 2467–2472. DOI: https://doi.org/10.1109/CDC.2004.1428782
- TERRELL, W. J. (2009) Stability and Stabilization: An Introduction. Princeton University Press, Princeton.
- XIE, D., YUAN, D., LU, J. and ZHANG, Y. (2013) Consensus control of second-order leader–follower multi-agent systems with event-triggered strategy. Transactions of the Institute of Measurement and Control 35 (4), 426–436. DOI: https://doi.org/10.1177/0142331212454046
- YAZICIO ˇGLU, A. Y. and EGERSTEDT, M. (2013) Leader selection and network assembly for controllability of leader–follower networks. American Control Conference, 3802–3807. DOI: https://doi.org/10.1109/ACC.2013.6580419
- YU, W., REN, W., ZHENG, W. X., Chen, G. and LÜ, J. (2013) Distributed control gains design for consensus in multi-agent systems with second-order nonlinear dynamics. Automatica 49 (7), 2107–2115. DOI: https://doi.org/10.1016/j.automatica.2013.03.005
- ZHANG, L., SUN, J. and YANG, Q. (2021) Distributed model-based event-triggered leader–follower consensus control for linear continuous-time multiagent systems. IEEE Transactions on Systems, Man, and Cybernetics: Systems 51 (10), 6457–6465. DOI: https://doi.org/10.1109/TSMC.2019.2962735
- ZHENG, Y. and WANG, L. (2012) Finite-time consensus of heterogeneous multi-agent systems with and without velocity measurements. Systems & Control Letters 61 (8), 871–878. DOI: https://doi.org/10.1016/j.sysconle.2012.05.009
- ZHENG, Y. and WANG, L. (2012) Distributed consensus of heterogeneous multi-agent systems with fixed and switching topologies. International Journal of Control 85 (12), 1967–1976. DOI: https://doi.org/10.1080/00207179.2012.713986
- ZHENG, Y., ZHU, Y. and WANG, L. (2011) Consensus of heterogeneous multi-agent systems. IET Control Theory & Applications 5 (16), 1881–1888. DOI: https://doi.org/10.1049/iet-cta.2011.0033