Consensus of high-order linear systems using dynamic output feedback compensator: low gain approach. (English) Zbl 1180.93005

Summary: We study the consensus (and synchronization) problem for multi-agent linear dynamic systems. All the agents have identical MIMO linear dynamics which can be of any order, and only the output information of each agents is delivered throughout the communication network. It is shown that consensus is reached if there exists a stable compensator which simultaneously stabilizes \(N - 1\) systems in a special form, where \(N\) is the number of agents. We show that there exists such a compensator under a very general condition. Finally, the consensus value is characterized as a function of initial conditions with stable compensators in place.


93A14 Decentralized systems
93B50 Synthesis problems
90B18 Communication networks in operations research
93C05 Linear systems in control theory
Full Text: DOI


[1] Fax, J.A.; Murray, R.M., Information flow and cooperative control of vehicle formations, IEEE transactions on automatic control, 49, 9, 1465-1476, (2004) · Zbl 1365.90056
[2] Hara, S., Hayakawa, T., & Sugata, H. (2007). Stability analysis of linear systems with generalized frequency variables and its application to formation control. In Proc. of the conf. on decision and control (pp. 1459-1466)
[3] Jadbabaie, A.; Lin, J.; Morse, A.S., Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE transactions on automatic control, 48, 6, 998-1001, (2003) · Zbl 1364.93514
[4] Kim, T. -H., & Hara, S. (2008). Stabilization of multi-agent dynamical systems for cyclic pursuit behavior. In Proc. of the conf. on decision and control (pp. 4370-4375)
[5] Lancaster, P.; Tismenetsky, M., The theory of matrices, (1985), Academic Press · Zbl 0516.15018
[6] Lin, Z., Low gain feedback, (1999), Springer
[7] Olfati-Saber, R.; Fax, J.A.; Murray, R.M., Consensus and cooperation in networked multi-agent systems, Proceedings of the IEEE, 95, 1, 215-233, (2007) · Zbl 1376.68138
[8] Pecora, L.M.; Carroll, T.L., Master stability functions for synchronized coupled systems, Physical review letters, 80, 10, 2109-2112, (1998)
[9] Ren, W., On consensus algorithms for double-integrator dynamics, IEEE transactions on automatic control, 53, 6, 1503-1509, (2008) · Zbl 1367.93567
[10] Ren, W., Moore, K., & Chen, Y. (2006). High-order consensus algorithms in cooperative vehicle systems. In Proc. of int. conf. on networking, sensing and control (pp. 457-462)
[11] Ren, W.; Beard, R.W.; Atkins, E.M., Information consensus in multivehicle cooperative control: collective group behavior through local interaction, IEEE control systems magazine, 27, 2, 71-82, (2007)
[12] Scardovi, L., & Sepulchre, R. (2008). Synchronization in networks of identical linear systems. In Proc. of conf. on decision and control (pp. 546-551) · Zbl 1183.93054
[13] Seo, J. H., Shim, H., & Back, J. (2009a). Consensus and synchronization of linear high-order systems via output coupling. In Proc. of European control conference (pp. 767-772)
[14] Seo, J. H., Shim, H., & Back, J. (2009b). High-order consensus of MIMO linear dynamic systems via stable compensator. In Proc. of European control conference (pp. 773-778)
[15] Tuna, S.E., Synchronizing linear systems via partial-state coupling, Automatica, 44, 8, 2179-2184, (2008) · Zbl 1283.93028
[16] Tuna, S. E. (2008b). Conditions for synchronizability in arrays of coupled linear systems. arXiv:0811.3530v1 [math.DS] (available from http://arxiv.org/abs/0811.3530)
[17] Wang, J.; Cheng, A.; Hu, X., Consensus of multi-agent linear dynamic systems, Asian journal of control, 10, 2, 144-155, (2008)
[18] Wieland, P., Kim, J. -S., Scheu, H., & Allgöwer, F. (2008). On consensus in multi-agent systems with linear high-order agents. In Proc. 17th IFAC world congress (pp. 1541-1546)
[19] Willems, J.C., Least square stationary optimal control and the algebraic Riccati equation, IEEE transactions on automatic control, 26, 6, 621-634, (1971)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.