Abstract
A nonconservative stability theory for switched linear systems is applied to the convergence analysis of consensus algorithms in the discrete-time domain. It is shown that the uniform-joint-connectedness condition for asymptotic consensus in distributed asynchronous algorithms and multi-particle models is in fact necessary and sufficient for uniform exponential consensus.
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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)
Ren, W., Beard, R.W., Atkins, E.M.: Information consensus in multivehicle cooperative control. IEEE Control Systems Magazine 27(2), 71–82 (2007)
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), 988–1001 (2003)
Branicky, M.S.: Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Transactions on Automatic Control 43(4), 475–482 (1998)
Liberzon, D., Morse, A.S.: Basic problems in stability and design of switched systems. Control Systems Magazine 19(5), 59–70 (1999)
DeCarlo, R.A., Branicky, M.S., Pettersson, S., Lennartson, B.: Perspectives and results on the stability and stabilizability of hybrid systems. Proceedings of the IEEE 88(7), 1069–1082 (2000)
Sun, Z., Ge, S.S.: Analysis and synthesis of switched linear control systems. Automatica 41(2), 181–195 (2005)
Tsitsiklis, J.N., Bertsekas, D.P., Athans, M.: Distributed asynchronous deterministic and stochastic gradient optimization algorithms. IEEE Transactions on Automatic Control 31(9), 803–812 (1986)
Ren, W., Beard, R.W.: Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Transactions on Automatic Control 50(5), 655–661 (2005)
Moreau, L.: Stability of multiagent systems with time-dependent communication links. IEEE Transactions on Automatic Control 50(2), 169–182 (2005)
Lee, J.W., Dullerud, G.E.: Uniform stabilization of discrete-time switched and Markovian jump linear systems. Automatica 42(2), 205–218 (2006)
Lee, J.W., Dullerud, G.E.: Optimal disturbance attenuation for discrete-time switched and Markovian jump linear systems. SIAM Journal on Control and Optimization 45(4), 1329–1358 (2006)
Lee, J.W., Dullerud, G.E.: Uniformly stabilizing sets of switching sequences for switched linear systems. IEEE Transactions on Automatic Control 52(5), 868–874 (2007)
Vicsek, T., Czirók, A., Ben-Jacob, E., Cohen, I., Shochet, O.: Novel type of phase transition in a system of self-driven particles. Physical Review Letters 75(6), 1226–1229 (1995)
Bertsekas, D.P., Tsitsiklis, J.N.: Comments on coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Transactions on Automatic Control 52(5), 968–969 (2007)
Daubechies, I., Lagarias, J.C.: Sets of matrices all infinite products of which converge. Linear Algebra and its Applications 161, 227–263 (1992)
Berger, M.A., Wang, Y.: Bounded semigroups of matrices. Linear Algebra and its Applications 166, 21–27 (1992)
Gurvits, L.: Stability of discrete linear inclusion. Linear Algebra and its Applications 231, 47–85 (1995)
Daubechies, I., Lagarias, J.C.: Corrigendum/addendum to: Sets of matrices all infinite products of which converge. Linear Algebra and its Applications 327, 69–83 (2001)
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Lee, JW. (2009). Uniform Consensus among Self-driven Particles. In: Majumdar, R., Tabuada, P. (eds) Hybrid Systems: Computation and Control. HSCC 2009. Lecture Notes in Computer Science, vol 5469. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00602-9_18
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DOI: https://doi.org/10.1007/978-3-642-00602-9_18
Publisher Name: Springer, Berlin, Heidelberg
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