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Synchronization in networks of identical linear systems. (English) Zbl 1183.93054
Summary: The paper investigates the synchronization of a network of identical linear state-space models under a possibly time-varying and directed interconnection structure. The main result is the construction of a dynamic output feedback coupling that achieves synchronization if the decoupled systems have no exponentially unstable mode and if the communication graph is uniformly connected. The result can be interpreted as a generalization of classical consensus algorithms. Stronger conditions are shown to be sufficient -- but to some extent, also necessary -- to ensure synchronization with the diffusive static output coupling often considered in the literature.

MSC:
93B50Synthesis problems
93C05Linear control systems
93A14Decentralized systems
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References:
[1] Arcak, M.: Passivity as a design tool for group coordination, IEEE transactions on automatic control 52, No. 18, 1380-1390 (2007)
[2] , Periodic control systems 2001 (2001)
[3] Carli, R., Chiuso, A., Schenato, L., & Zampieri, S. (2008). A pi consensus controller for networked clocks synchronization. In 17th IFAC world congress
[4] Hale, J. K.: Diffusive coupling, dissipation, and synchronization, Journal of dynamics and differential equations 9, No. 1, 1-52 (1996) · Zbl 1091.34532 · doi:10.1007/BF02219051
[5] Horn, R. A.; Johnson, C. R.: Topics in matrix analysis, (1994) · Zbl 0801.15001
[6] Jadbabaie, A.; Lin, J.; Morse, S.: Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE transactions on automatic control 48, 988-1001 (2003)
[7] Loria, A.; Panteley, E.; Popovic, D.; Teel, A.: A nested matrosov theorem and persistency of excitation for uniform convergence in stable nonautonomous systems, IEEE transactions on automatic control 50, No. 2, 183--198 (2005)
[8] Moreau, L.: Stability of multi-agent systems with time-dependent communication links, IEEE transactions on automatic control 50, No. 2, 169-182 (2005)
[9] Moreau, L. (2004). Stability of continuous-time distributed consensus algorithms. In Proceedings of the 43rd IEEE conference on decision and control, (pp. 3998-4003)
[10] Nair, S.; Leonard, N.: Stable synchronization of mechanical system networks, SIAM journal on control and optimization 47, No. 2, 661-683 (2008) · Zbl 1158.70013 · doi:10.1137/050646639
[11] Olfati-Saber, R.; Murray, R.: Consensus problems in networks of agents with switching topology and time-delays, IEEE transactions on automatic control 49, No. 9, 1520-1533 (2004)
[12] Pham, Q. C.; Slotine, J. -J.: Stable concurrent synchronization in dynamic system networks, Neural networks 20, No. 1, 62-77 (2007) · Zbl 1158.68449 · doi:10.1016/j.neunet.2006.07.008
[13] Pogromsky, A.: Passivity based design of synchronizing systems, International journal of bifurcation and chaos 8, No. 2, 295-319 (1998) · Zbl 0938.93056 · doi:10.1142/S0218127498000188
[14] Ren, W.: On consensus algorithms for double-integrator dynamics, IEEE transactions on automatic control 53, No. 6, 1503-1509 (2008)
[15] Sarlette, A., Sepulchre, R., & Leonard, N. (2007). Autonomous rigid body attitude synchronization. In Proceedings of the 46th IEEE conference on decision and control, (pp. 2566-2571 · Zbl 1158.93372
[16] Scardovi, L.; Leonard, N.; Sepulchre, R.: Stabilization of collective motion in three-dimensions, Communications in information and systems 8, No. 3, 473-500 (2008) · Zbl 1168.93007
[17] Scardovi, L.; Sarlette, A.; Sepulchre, R.: Synchronization and balancing on the N-torus, Systems and control letters 56, No. 5, 335-341 (2007) · Zbl 1111.68007 · doi:10.1016/j.sysconle.2006.10.020
[18] Scardovi, L., & Sepulchre, R. (2008). Synchronization in networks of identical linear systems. arXiv:0805.3456v1 [Online]. Available: http://arxiv.org/abs/0805.3456 · Zbl 1183.93054
[19] Sepulchre, R.; Paley, D.; Leonard, N.: Stabilization of planar collective motion with limited communication, IEEE transactions on automatic control 53, No. 3, 706-719 (2008)
[20] Stan, G. B.; Sepulchre, R.: Analysis of interconnected oscillators by dissipativity theory, IEEE transactions on automatic control 52, No. 2, 256-270 (2007)
[21] Tuna, E. S.: Synchronizing linear systems via partial-state coupling, Automatica 44, 2179-2184 (2008) · Zbl 1283.93028
[22] Willems, J. C.: Lyapunov functions for diagonally dominant systems, Automatica. A journal IFAC 12, No. 5, 519-523 (1976) · Zbl 0345.93040 · doi:10.1016/0005-1098(76)90011-X