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Leader-following consensus of multiple linear systems under switching topologies: An averaging method
Kybernetika, Tome 48 (2012) no. 6, pp. 1194-1210 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The leader-following consensus of multiple linear time invariant (LTI) systems under switching topology is considered. The leader-following consensus problem consists of designing for each agent a distributed protocol to make all agents track a leader vehicle, which has the same LTI dynamics as the agents. The interaction topology describing the information exchange of these agents is time-varying. An averaging method is proposed. Unlike the existing results in the literatures which assume the LTI agents to be neutrally stable, we relax this condition, only making assumption that the LTI agents are stablizable and detectable. Observer-based leader-following consensus is also considered.
The leader-following consensus of multiple linear time invariant (LTI) systems under switching topology is considered. The leader-following consensus problem consists of designing for each agent a distributed protocol to make all agents track a leader vehicle, which has the same LTI dynamics as the agents. The interaction topology describing the information exchange of these agents is time-varying. An averaging method is proposed. Unlike the existing results in the literatures which assume the LTI agents to be neutrally stable, we relax this condition, only making assumption that the LTI agents are stablizable and detectable. Observer-based leader-following consensus is also considered.
Classification : 93C15, 93C35
Keywords: consensus; multi-agent systems; averaging method 
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Ni, Wei; Wang, Xiaoli; Xiong, Chun. Leader-following consensus of multiple linear systems under switching topologies: An averaging method. Kybernetika, Tome 48 (2012) no. 6, pp. 1194-1210. http://geodesic.mathdoc.fr/item/KYB_2012_48_6_a7/

[1] Aeyels, D., Peuteman, J.: On xponential stability of nonlinear time-varying differential equations. Automatica 35 (1999), 1091-1100. | DOI | MR

[2] Bellman, R., Bentsman, J., Meerkov, S. M.: Stability of fast periodic systems. IEEE Trans. Automat. Control 30 (1985), 289-291. | DOI | MR | Zbl

[3] Bogoliubov, N. N., Mitropolsky, Y. A.: Asymptotic Methods in the Theory of Nonlinear Oscillations. Gordon and Breach, New York 1961. | MR

[4] Cheng, D., Wang, J. H., Hu, X.: An extension of LaSalle's invariance principle and its application to multi-agent consensus. IEEE Trans. Automat. Control 53 (2008), 1765-1770. | DOI | MR

[5] Hong, Y., Gao, L., Cheng, D., Hu, J.: Lyapunov-based approach to multiagent systems with switching jointly connected interconnection. IEEE Trans. Automat. Control 52 (2007), 943-948. | DOI | MR

[6] Hong, Y., Hu, J., Gao, L.: Tracking control for multiagent consensus with an active leader and variable topology. Automatica 42 (2006), 1177-1182. | DOI | MR

[7] Horn, R., Johnson, C.: Matrix Analysis. Cambridge University Press, New York 1985. | MR | Zbl

[8] Jadbabaie, A., Lin, J., Morse, A. S.: Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans. Automat. Control 48 (2003), 943-948. | MR

[9] Khoo, S., Xie, L., Man, Z., Zhao, S.: Observer-based robust finite-time cooperative consensus control for multi-agent networks. In: Proc. 4th IEEE Conference on Industrial Electronics and Applications, Xi'an 2009, pp. 1883-1888.

[10] Kosut, R. L., Anderson, B. D. O., Mareels, I. M. Y.: Stability theory for adaptive systems: method of averaging and persistency of excitation. IEEE Trans. Automat. Control 32 (1987), 26-34. | DOI | MR

[11] Krasnosel'skii, M. A., Krein, S. G.: On The Averaging Principle in Nonlinear Mechanics. Uspekhi Matem Nauk, 1955.

[12] Krylov, N., Bogoliubov, N.: Introduction to Non-Linear Mechnnics. Princeton University Press, Princeton 1949.

[13] Liu, Y., Jia, Y., Du, J., Yuan, S.: Dynamic output feedback control for consensus of multi-agent systems: an $H_\infty$ approach. In: Proc. American Control Conference, St. Louis 2009, pp. 4470-4475.

[14] Namerikawa, T., Yoshioka, C.: Consensus control of observer-based multi-agent system with communication delay. In: Proc. SICE Annual Conference, Tokyo 2008, pp. 2414-2419.

[15] Ni, W., Cheng, D.: Leader-following consensus of multi-agent systems under fixed and switching topologies. Systems Control Lett. 59 (2010), 209-217. | DOI | MR

[16] Olfati-Saber, R., Murray, R. M.: Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Automat. Control 49 (2004), 1520-1533. | DOI | MR

[17] Olfati-Saber, R., Fax, J. A., Murray, R. M.: Consensus and cooperation in networked multi-agent systems. Proc. IEEE 95 (2007), 215-233.

[18] Ren, W., Beard, R. W.: Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Trans. Automat. Control 50 (2005), 655-661. | DOI | MR

[19] Ren, W., Beard, R. W., Atkins, E.: Information consensus in multivehicle cooperative control. IEEE Control Syst. Mag. 27 (2007), 71-82. | DOI

[20] Sanders, J. A., Verhulst, F., Murdock, J.: Averaging Methods in Nonlinear Dynamical Systems. Second edition. Springer, New York 2007. | MR

[21] Seo, J. H., Shima, H., Back, J.: Consensus of high-order linear systems using dynamic output feedback compensator: low gain approach. Automatica 45 (2009), 2659-2664. | DOI | MR

[22] Scardovi, L., Sepulchre, R.: Synchronization in networks of identical linear systems. Automatica 45 (2009), 2557-2562. | DOI | MR

[23] Stilwell, D. J., Bellt, E. M., Roberson, D. G.: Sufficient conditions for fast switching sysnchronization in time-varying network topologies. SIAM J. Appl. Dynam. Syst. 5 (2006), 140-157. | DOI | MR

[24] Teel, A. R., Nesic, D.: Averaging for a class of hybrid systems. Dynamics Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 17 (2010), 829-851. | MR

[25] Wang, J., Cheng, D., Hu, X.: Consensus of multi-agent linear dynamical systems. Asian J. Control 10 (2008), 144-155. | DOI | MR

[26] Wang, X., Hong, Y.: Parametrization and geometric analysis of coordination controllers for multi-agent systems. Kybernetika 45 (2009), 785-800. | MR | Zbl

[27] Wang, X., Hong, Y., Huang, J., Jiang, Z.: A distributed control approach to a robust output regulation problem for multi-agent linear systems. IEEE Trans. Automat. Control 55 (2010), 2891-2895. | DOI | MR

[28] Wang, X., Han, F.: Robust coordination control of switching multi-agent systems via output regulation approach. Kybernetika 47 (2011), 755-772. | MR | Zbl

[29] Yoshioka, C., Namerikawa, T.: Observer-based consensus control strategy for multi-agent system with communication time delay. In: Proc. 17th IEEE International Conference on Control Applications, San Antonio 2008, pp. 1037-1042.

[30] Zhang, H., Lewis, F. L., Das, A.: Optimal design for synchronization of cooperative systems: state feedback, observer and output feedback. IEEE Trans. Automat. Control 56 (2011), 1948-1952. | DOI | MR