Improved frequency sweeping technique and stability analysis of the second-order consensus protocol with distributed delays

References

• Atay, F. M. (2013). The consensus problem in networks with transmission delays. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 371(1999), 20120460. https://doi.org/10.1098/rsta.2012.0460
   PubMed Web of Science ®Google Scholar
• Biggs, N. (1974). Algebraic graph theory (2nd ed.). Cambridge University Press.
   Google Scholar
• Canny, J., & Emiris, I. (1993). An efficient algorithm for the sparse mixed resultant. In G. Cohen, T. Mora, & O. Moreno (Eds.), Applied algebra, algebraic algorithms and error-correcting codes. Springer Berlin Heidelberg.
   Google Scholar
• Cepeda-Gomez, R., & Olgac, N. (2011a). An exact method for the stability analysis of linear consensus protocols with time delay. IEEE Transactions on Automatic Control, 56(7), 1734–1740. https://doi.org/10.1109/TAC.2011.2152510
   Web of Science ®Google Scholar
• Cepeda-Gomez, R., & Olgac, N. (2011b). Exhaustive stability analysis in a consensus system with time delay and irregular topologies. International Journal of Control, 84(4), 746–757. https://doi.org/10.1080/00207179.2011.576272
   Web of Science ®Google Scholar
• Cepeda-Gomez, R., & Olgac, N. (2013). Exact stability analysis of second-order leaderless and leader – follower consensus protocols with rationally-independent multiple time delays. Systems & Control Letters, 62(6), 482–495. https://doi.org/10.1016/j.sysconle.2013.02.011
   Web of Science ®Google Scholar
• Chen, J., & Latchman, H. A. (1995). Frequency sweeping tests for stability independent of delay. IEEE Transactions on Automatic Control, 40(9), 1640–1645. https://doi.org/10.1109/9.412637
   Web of Science ®Google Scholar
• Dixon, A. L. (1909). The eliminant of three quantics in two independent variables. Proceedings of the London Mathematical Society, 2(1), 49–69. https://doi.org/10.1112/plms/s2-7.1.49
   Google Scholar
• Dong, C., Gao, Q., Xiao, Q., Chu, R., & Jia, H. (2020). Spectrum-domain stability assessment and intrinsic oscillation for aggregated mobile energy storage in grid frequency regulation. Applied Energy, 276, Article 115434. https://doi.org/10.1016/j.apenergy.2020.115434
   PubMed Web of Science ®Google Scholar
• Dong, C., Gao, Q., Xiao, Q., Yu, X., Pekař, L., & Jia, H. (2018). Time-delay stability switching boundary determination for DC microgrid clusters with the distributed control framework. Applied Energy, 228, 189–204. https://doi.org/10.1016/j.apenergy.2018.06.026
   Web of Science ®Google Scholar
• Ergenc, A. F., Olgac, N., & Fazelinia, H. (2007). Extended Kronecker summation for cluster treatment of LTI systems with multiple delays. SIAM Journal on Control and Optimization, 46(1), 143–155. https://doi.org/10.1137/06065180X
   Web of Science ®Google Scholar
• Fazelinia, H., Sipahi, R., & Olgac, N. (2007). Stability robustness analysis of multiple time-delayed systems using “building block” concept. IEEE Transactions on Automatic Control, 52(5), 799–810. https://doi.org/10.1109/TAC.2007.898076
   Web of Science ®Google Scholar
• Gao, Q., Kammer, A. S., Zalluhoglu, U., & Olgac, N. (2015a). Combination of sign inverting and delay scheduling control concepts for multiple-delay dynamics. Systems & Control Letters, 77, 55–62. https://doi.org/10.1016/j.sysconle.2015.01.001
   Web of Science ®Google Scholar
• Gao, Q., Kammer, A. S., Zalluhoglu, U., & Olgac, N. (2015b). Critical effects of the polarity change in delayed states within an LTI dynamics with multiple delays. IEEE Transactions on Automatic Control, 60(11), 3018–3022. https://doi.org/10.1109/TAC.2015.2408553
   Web of Science ®Google Scholar
• Gao, Q., & Olgac, N. (2015). Optimal sign inverting control for time-delayed systems, a concept study with experiments. International Journal of Control, 88(1), 113–122. https://doi.org/10.1080/00207179.2014.941409
   Web of Science ®Google Scholar
• Gao, Q., & Olgac, N. (2016). Bounds of imaginary spectra of LTI systems in the domain of two of the multiple time delays. Automatica, 72, 235–241. https://doi.org/10.1016/j.automatica.2016.05.011
   Web of Science ®Google Scholar
• Kammer, A., & Olgac, N. (2015). Non-conservative stability assessment of LTI dynamics with distributed delay using CTCR paradigm. Proceedings of the American Control Conference, 2015, 4597–4602. https://doi.org/10.1109/ACC.2015.7172053
   Google Scholar
• Kapur, D., & Saxena, T. (1995). Comparison of various multivariate resultant formulations. In Proceedings of the 1995 international symposium on symbolic and algebraic computation. Association for Computing Machinery.
   Google Scholar
• Kapur, D., Saxena, T., & Yang, L. (1994). Algebraic and geometric reasoning using dixon resultants. In Proceedings of the international symposium on symbolic and algebraic computation. Association for Computing Machinery.
   Google Scholar
• Macaulay, F. S. (1994). The algebraic theory of modular systems (Vol. 19). Cambridge University Press.
   Google Scholar
• Michiels, W., Morărescu, C. I., & Niculescu, S. I. (2009). Consensus problems with distributed delays, with application to traffic flow models. SIAM Journal on Control and Optimization, 48(1), 77–101. https://doi.org/10.1137/060671425
   Web of Science ®Google Scholar
• Moreau, L. (2005). Stability of multiagent systems with time-dependent communication links. IEEE Transactions on Automatic Control, 50(2), 169–182. https://doi.org/10.1109/TAC.2004.841888
   Web of Science ®Google Scholar
• Norkin, S. B. (1973). Introduction to the theory and application of differential equations with deviating arguments. Academic Press.
   Google Scholar
• Olfati-Saber, R., & R. M. Murray (2004). Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on Automatic Control, 49(9), 1520–1533. https://doi.org/10.1109/TAC.2004.834113
   Web of Science ®Google Scholar
• Olgac, N., & Kammer, A. S. (2014). Stabilisation of open-loop unstable plants under feedback control with distributed delays. IET Control Theory & Applications, 8(10), 813–820. https://doi.org/10.1049/cth2.v8.10
   Web of Science ®Google Scholar
• Olgac, N., & Sipahi, R. (2002). An exact method for the stability analysis of time-delayed linear time-invariant (LTI) systems. IEEE Transactions on Automatic Control, 47(5), 793–797. https://doi.org/10.1109/TAC.2002.1000275
   Web of Science ®Google Scholar
• Özbay, H., Bonnet, C., Benjelloun, H., & Clairambault, J. (2012). Stability analysis of cell dynamics in leukemia. Mathematical Modelling of Natural Phenomena, 7(1), 203–234. https://doi.org/10.1051/mmnp/20127109
   Web of Science ®Google Scholar
• Ren, W., & Beard, R. W. (2005). Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Transactions on Automatic Control, 50(5), 655–661. https://doi.org/10.1109/TAC.2005.846556
   Web of Science ®Google Scholar
• Richard, J. P. (2003). Time-delay systems: An overview of some recent advances and open problems. automatica, 39(10), 1667–1694. https://doi.org/10.1016/S0005-1098(03)00167-5
   Web of Science ®Google Scholar
• Schafer, R. D. (2017). An introduction to nonassociative algebras. Courier Dover Publications.
   Google Scholar
• Sergienko, I., & Galba, E. (2003). Limiting representations of weighted pseudoinverse matrices with positive definite weights. Problem regularization. Cybernetics and Systems Analysis, 39(6), 816–830. https://doi.org/10.1023/B:CASA.0000020223.16135.82
   Google Scholar
• Shang, Y. (2017). On the delayed scaled consensus problems. Applied Sciences, 7(7), 713. https://doi.org/10.3390/app7070713
   Google Scholar
• Shao, J., Zheng, W. X., Huang, T. Z., & Bishop, A. N. (2018). On leader – follower consensus with switching topologies: An analysis inspired by pigeon hierarchies. IEEE Transactions on Automatic Control, 63(10), 3588–3593. https://doi.org/10.1109/TAC.9
   Web of Science ®Google Scholar
• Sipahi, R., & Olgac, N. (2005). Complete stability robustness of third-order LTI multiple time-delay systems. Automatica, 41(8), 1413–1422. https://doi.org/10.1016/j.automatica.2005.03.022
   Web of Science ®Google Scholar
• Sun, Y. G., & Wang, L. (2009). Consensus problems in networks of agents with double-integrator dynamics and time-varying delays. International Journal of Control, 82(10), 1937–1945. https://doi.org/10.1080/00207170902838269
   Web of Science ®Google Scholar
• Toker, O., & Özbay, H. (1996). Complexity issues in robust stability of linear delay-differential systems. Mathematics of Control, Signals, and Systems, 9(4), 386–400. https://doi.org/10.1007/BF01211858
   Web of Science ®Google Scholar
• Trott, M. (2006). The mathematica guidebook for numerics. Springer Science & Business Media.
   Google Scholar
• Vyhlídal, T., Hromčík, M., Kučera, V., & Anderle, M. (2016). On feedback architectures with zero-vibration signal shapers. IEEE Transactions on Automatic Control, 61(8), 2049–2064. https://doi.org/10.1109/TAC.2015.2492502
   Web of Science ®Google Scholar
• Vyhlidal, T., & Zítek, P. (2009). Mapping based algorithm for large-scale computation of quasi-polynomial zeros. IEEE Transactions on Automatic Control, 54(1), 171–177. https://doi.org/10.1109/TAC.2008.2008345
   Web of Science ®Google Scholar
• Yang, R., Liu, S., Tan, Y. Y., Zhang, Y. J., & Jiang, W. (2019). Consensus analysis of fractional-order nonlinear multi-agent systems with distributed and input delays. Neurocomputing, 329, 46–52. https://doi.org/10.1016/j.neucom.2018.10.045
   Web of Science ®Google Scholar