×

zbMATH — the first resource for mathematics

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:
93B50 Synthesis problems
93C05 Linear systems in control theory
93A14 Decentralized systems
PDF BibTeX XML Cite
Full Text: DOI arXiv
References:
[1] Arcak, M., Passivity as a design tool for group coordination, IEEE transactions on automatic control, 52, 18, 1380-1390, (2007) · Zbl 1366.93563
[2] ()
[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, 1, 1-52, (1996) · Zbl 1091.34532
[5] Horn, R.A.; Johnson, C.R., Topics in matrix analysis, (1994), Cambridge University Press · 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) · Zbl 1364.93514
[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, 2, 183–198, (2005) · Zbl 1365.93471
[8] Moreau, L., Stability of multi-agent systems with time-dependent communication links, IEEE transactions on automatic control, 50, 2, 169-182, (2005) · Zbl 1365.93268
[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, 2, 661-683, (2008) · Zbl 1158.70013
[11] Olfati-Saber, R.; Murray, R., Consensus problems in networks of agents with switching topology and time-delays, IEEE transactions on automatic control, 49, 9, 1520-1533, (2004) · Zbl 1365.93301
[12] Pham, Q.C.; Slotine, J.-J., Stable concurrent synchronization in dynamic system networks, Neural networks, 20, 1, 62-77, (2007) · Zbl 1158.68449
[13] Pogromsky, A., Passivity based design of synchronizing systems, International journal of bifurcation and chaos, 8, 2, 295-319, (1998) · Zbl 0938.93056
[14] Ren, W., On consensus algorithms for double-integrator dynamics, IEEE transactions on automatic control, 53, 6, 1503-1509, (2008) · Zbl 1367.93567
[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, 3, 473-500, (2008), (Special issue dedicated to the 70th birthday of Roger W. Brockett) · Zbl 1168.93007
[17] Scardovi, L.; Sarlette, A.; Sepulchre, R., Synchronization and balancing on the \(N\)-torus, Systems and control letters, 56, 5, 335-341, (2007) · Zbl 1111.68007
[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, 3, 706-719, (2008) · Zbl 1367.93145
[20] Stan, G.B.; Sepulchre, R., Analysis of interconnected oscillators by dissipativity theory, IEEE transactions on automatic control, 52, 2, 256-270, (2007) · Zbl 1366.34054
[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, 5, 519-523, (1976) · Zbl 0345.93040
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.