The Distribution of Zeros of Quasi-Polynomials

Honghai Wang; Qing-Long Han

doi:10.1109/JAS.2023.123597

Volume 10 Issue 2

Feb. 2023

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2023 > 10(2): 301-304

H. H. Wang and Q.-L. Han, “The distribution of zeros of quasi-polynomials,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 2, pp. 301–304, Feb. 2023. doi: 10.1109/JAS.2023.123597

Citation:

H. H. Wang and Q.-L. Han, “The distribution of zeros of quasi-polynomials,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 2, pp. 301–304, Feb. 2023. doi: 10.1109/JAS.2023.123597

H. H. Wang and Q.-L. Han, “The distribution of zeros of quasi-polynomials,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 2, pp. 301–304, Feb. 2023. doi: 10.1109/JAS.2023.123597

Citation:

H. H. Wang and Q.-L. Han, “The distribution of zeros of quasi-polynomials,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 2, pp. 301–304, Feb. 2023. doi: 10.1109/JAS.2023.123597

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The Distribution of Zeros of Quasi-Polynomials

doi: 10.1109/JAS.2023.123597

Honghai Wang^1
,,
Qing-Long Han^2
,

1.
College of Information Science and Engineering,Northeastern University, Shenyang 110004, China
2.
School of Science, Computing and Engineering Technologies, Swinburne University of Technology, Melbourne, VIC 3122, Australia

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Author Bio:
Honghai Wang received the B.S. degree in Automation, the M.S. degree and the PhD degree in Control Theory and Control Engineering from Northeastern University, Shenyang, China, in 2006, 2008 and 2015, respectively. From 2015 to 2017, he was a Postdoctoral Research Fellow with the College of Computer Science and Engineering, Northeastern University. From 2018 to 2019, he was a Visiting Scholar at Swinburne University of Technology, Melbourne, VIC, Australia. He is currently an Associate Professor with the College of Information Science and Engineering at the Northeastern University. His current research interests include time delay systems, discrete-time systems, networked control systems, multi-agent systems, and PID control

Qing-Long Han (Fellow, IEEE) received the B.Sc. degree in Mathematics from Shandong Normal University, Jinan, China, in 1983, and the M.Sc. and Ph.D. degrees in Control Engineering from East China University of Science and Technology, Shanghai, China, in 1992 and 1997, respectively. Professor Han is Pro Vice-Chancellor (Research Quality) and a Distinguished Professor at Swinburne University of Technology, Melbourne, Australia. He held various academic and management positions at Griffith University and Central Queensland University, Australia. His research interests include networked control systems, multi-agent systems, time-delay systems, smart grids, unmanned surface vehicles, and neural networks. Professor Han was awarded The 2021 Norbert Wiener Award (the Highest Award in systems science and engineering, and cybernetics) and The 2021 M. A. Sargent Medal (the Highest Award of the Electrical College Board of Engineers Australia). He was the recipient of The 2022 IEEE Systems, Man, and Cybernetics Society Andrew P. Sage Best Transactions Paper Award, The 2021 IEEE/CAA Journal of Automatica Sinica Norbert Wiener Review Award, The 2020 IEEE Systems, Man, and Cybernetics Society Andrew P. Sage Best Transactions Paper Award, The 2020 IEEE Transactions on Industrial Informatics Outstanding Paper Award, and The 2019 IEEE Systems, Man, and Cybernetics Society Andrew P. Sage Best Transactions Paper Award. Professor Han is a Member of the Academia Europaea (The Academy of Europe). He is a Fellow of The International Federation of Automatic Control (IFAC) and a Fellow of The Institution of Engineers Australia (IEAust). He is a Highly Cited Researcher in both Engineering and Computer Science (Clarivate Analytics). He has served as an AdCom Member of IEEE Industrial Electronics Society (IES), a Member of IEEE IES Fellows Committee, and Chair of IEEE IES Technical Committee on Networked Control Systems. Currently, he is Editor-in-Chief of IEEE/CAA Journal of Automatica Sinica, Co-Editor-in-Chief of IEEE Transactions on Industrial Informatics, and Co-Editor of Australian Journal of Electrical and Electronic Engineering
Available Online: 2023-04-12

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References

[1]	Y. Zhang, “Discrete mean estimates and the Landau-Siegel zero,” arXiv, 2022, DOI: 10.48550/arxiv.2211.02515
[2]	F. Golnaraghi and B. C. Kuo, Automatic Control Systems (9th ed.), Wiley, 2010.
[3]	J. K. Hale and S. M. Verduyn Lunel, Introduction to Functional Differential Equations, New York: Springer-Verlag, 1993.
[4]	R. Sipahi, S.-I. Niculescu, C. T. Abdallah, W. Michiels, and K. Gu, “Stability and stabilization of systems with time delay,” IEEE Control Syst. Mag., vol. 31, no. 1, pp. 38–65, Jan. 2011. doi: 10.1109/MCS.2010.939135
[5]	X.-M. Zhang, Q.-L. Han, A. Seuret, F. Gouaisbaut, and Y. He, “Overview of recent advances in stability of linear systems with time-varying delays,” IET Contr. Theory Appl., vol. 13, no. 1, pp. 1–16, Jan. 2019. doi: 10.1049/iet-cta.2018.5188
[6]	W. Wang, “An overview of the recent advances in delay-time-based maintenance modelling,” Reliab. Eng. Syst. Saf., vol. 106, pp. 165–178, Oct. 2012. doi: 10.1016/j.ress.2012.04.004
[7]	H. Górecki, S. Fuksa, P. Grabowski, and A. Korytowski, Analysis and Synthesis of Time Delay Systems, Warszawa: Polish Scientific Publishers, 1989.
[8]	K. Gu, V. L. Kharitonov, and J. Chen, Stability of Time-Delay Systems, Boston: Birkhäuser, 2003.
[9]	G. J. Silva, A. Datta, and S. P. Bhattacharyya, PID Controllers for Time-Delay Systems, Boston: Birkhäuser, 2005.
[10]	W. Michiels and S.-I. Niculescu, Stability and Stabilization of Time-Delay Systems: An Eigenvalue-Based Approach, SIAM, 2007.
[11]	Lúcia Cossi, Introduction to Stability of Quasipolynomials, Time-Delay Systems, Prof. Dragutin Debeljkovic (Ed.), InTech, 2011, Available at: http://www.intechopen.com/books/time-delay-systems/introduction-to-stability-of-quasipolynomials.
[12]	H. Wang, J. Liu, and Y. Zhang, “New results on eigenvalue distribution and controller design for time delay systems,” IEEE Trans. Automat. Control, vol. 62, no. 6, pp. 2886–2901, Jun. 2017. doi: 10.1109/TAC.2016.2637002
[13]	H. Wang, Q.-L. Han. J. Liu, and D. He, “Discrete-time filter proportional-integral-derivative controller design for linear time-invariant systems,” Automatica, vol. 116, art no. 108918 (pp. 108918: 1-108918: 15), Jun. 2020.
[14]	L. S. Pontryagin, “On zeros of some transcendental functions (in Russian),” Izv. Akad. Nauk. SSSR Ser. Mat., vol. 6, no. 3, pp. 115–134, Mar. 1942.
[15]	L. S. Pontryagin, “On the zeros of some elementary transcendental functions. (in English),” Amer. Math. Soc. Transl., vol. 2, pp. 95–110, Jan. 1955.
[16]	M. S. Lee and C. S. Hsu, “On the τ-decomposition method of stability analysis for retarded dynamical systems,” SIAM J. Control, vol. 7, no. 2, pp. 242–259, May 1969. doi: 10.1137/0307017
[17]	K. L. Cooke and van den Driessche, “On zeroes of some transcendental equations,” Funkcialaj Ekvacioj, vol. 29, no. 1, pp. 77–90, Jan. 1986.
[18]	K. Walton and J. E. Marshall, “Direct method for TDS stability analysis,” IEE Proc.-Control Theory Appl., vol. 134, no. 2, pp. 101–107, Mar. 1987. doi: 10.1049/ip-d.1987.0018
[19]	N. Olgac and R. Sipahi, “An exact method for the stability analysis of time-delayed linear time-invariant (LTI) systems,” IEEE Trans. Automat. Control, vol. 47, no. 5, pp. 793–797, May 2002. doi: 10.1109/TAC.2002.1000275
[20]	R. Sipahi and N. Olgac, “Complete stability robustness of third-order LTI multiple time-delay systems,” Automatica, vol. 41, no. 8, pp. 1413–1422, Aug. 2005. doi: 10.1016/j.automatica.2005.03.022
[21]	P. Fu, S.-I. Niculescu, and J. Chen, “Stability of linear neutral time-delay systems: Exact conditions via matrix pencil solutions,” IEEE Trans. Automat. Control, vol. 51, no. 6, pp. 1063–1069, Jun. 2006. doi: 10.1109/TAC.2006.876804
[22]	R. Sipahi and I. I. Delice, “Extraction of 3D stability switching hypersurfaces of a time delay system with multiple fixed delays,” Automatica, vol. 45, no. 6, pp. 1449–1454, Jun. 2009. doi: 10.1016/j.automatica.2009.01.017
[23]	J. Chen, P. Fu, S.-I. Niculescu, and Z. Guan, “An eigenvalue perturbation approach to stability analysis, Part II: When will zeros of time-delay systems cross imaginary axis?” SIAM J. Control Optim., vol. 48, no. 8, pp. 5583–5605, Sep. 2010. doi: 10.1137/080741719
[24]	K. Gu and M. Naghnaeian, “Stability crossing set for systems with three delays,” IEEE Trans. Automat. Control, vol. 56, no. 1, pp. 11–26, Jan. 2011. doi: 10.1109/TAC.2010.2050162
[25]	X.-G. Li, S.-I. Niculescu, A. Çela, H.-H. Wang, and T.-Y. Cai, “On computing Puiseux series for multiple imaginary characteristic roots of LTI systems with commensurate delays,” IEEE Trans. Automat. Control, vol. 58, no. 5, pp. 1338–1343, May 2013. doi: 10.1109/TAC.2012.2226102
[26]	X.-G. Li, S.-I. Niculescu, A. Çela, L. Zhang and X. Li, “A frequency-sweeping framework for stability analysis of time-delay systems,” IEEE Trans. Automat. Control, vol. 62, no. 8, pp. 3701–3716, Aug. 2017. doi: 10.1109/TAC.2016.2633533
[27]	F. M. Asl and A. G. Ulsoy, “Analysis of a system of linear delay differential equations,” J. Dyn. Syst.,Meas.,Control, vol. 125, no. 2, pp. 215–223, Jun. 2003. doi: 10.1115/1.1568121
[28]	D. Breda, “On characteristic roots and stability charts of delay differential equations,” Int. J. Robust Nonlinear Control, vol. 22, no. 8, pp. 892–917, May 2012. doi: 10.1002/rnc.1734
[29]	K. Engelborghs, T. Luzyanina, and D. Roose, “Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL,” ACM Trans. Math. Softw., vol. 28, no. 1, pp. 1–21, Mar. 2002. doi: 10.1145/513001.513002
[30]	J.-P. Richard, “Time-delay systems: An overview of some recent advances and open problems,” Automatica, vol. 39, no. 10, pp. 1667–1694, Oct. 2003. doi: 10.1016/S0005-1098(03)00167-5
[31]	L. Pekař and Q. Gao, “Spectrum analysis of LTI continuous-time systems with constant delays: A literature overview of some recent results,” IEEE Access, vol. 6, pp. 35457–35491, Jul. 2018. doi: 10.1109/ACCESS.2018.2851453
[32]	W. Hou, M. Fu, H. Zhang, and Z. Wu, “Consensus conditions for general second-order multi-agent systems with communication delay,” Automatica, vol. 75, pp. 293–298, Jan. 2017. doi: 10.1016/j.automatica.2016.09.042
[33]	R. Sipahi and N. Olgac, “A unique methodology for the stability robustness of multiple time delay systems,” Syst. Control Lett., vol. 55, no. 10, pp. 819–825, Oct. 2006. doi: 10.1016/j.sysconle.2006.03.010
[34]	R. Sipahi and N. Olgac, “Complete stability analysis of neutral-type first order two-time-delay systems with cross-talking delays,” SIAM J. Control Optim., vol. 45, no. 3, pp. 957–971, Mar. 2006. doi: 10.1137/050633810
[35]	N. Olgac, T. Vyhlídal, and R. Sipahi, “A new perspective in the stability assessment of neutral systems with multiple and cross-talking delays,” SIAM J. Control Optim., vol. 47, no. 1, pp. 327–344, Jan. 2008. doi: 10.1137/070679302
[36]	K. Gu, S.-I. Niculescu, and J. Chen, “On stability crossing curves for general systems with two delays,” J. Math. Anal. Appl., vol. 311, no. 1, pp. 231–253, Nov. 2005. doi: 10.1016/j.jmaa.2005.02.034
[37]	G. J. Silva, A. Datta, and S. P. Bhattacharyya, “PI stabilization of first-order systems with time delay,” Automatica, vol. 37, no. 12, pp. 2025–2031, Dec. 2001. doi: 10.1016/S0005-1098(01)00165-0
[38]	G. J. Silva, A. Datta, and S. P. Bhattacharyya, “New results on the synthesis of PID controllers,” IEEE Trans. Automat. Control, vol. 47, no. 2, pp. 241–252, Feb. 2002. doi: 10.1109/9.983352
[39]	V. A. Oliveira, M. C. M. Teixeira, and L. Cossi, “Stabilizing a class of time delay systems using the Hermite-Biehler theorem,” Linear Algebra Appl., vol. 369, pp. 203–216, Aug. 2003. doi: 10.1016/S0024-3795(02)00721-8
[40]	V. A. Oliveira, L. V. Cossi, M. C. M. Teixeira, and A. M. F. Silva, “Synthesis of PID controllers for a class of time delay systems,” Automatica, vol. 45, no. 7, pp. 1778–1782, Jul. 2009. doi: 10.1016/j.automatica.2009.03.018
[41]	L. Ou, W. Zhang, and L. Yu, “Low-order stabilization of LTI systems with time delay,” IEEE Trans. Automat. Control, vol. 54, no. 4, pp. 774–787, Apr. 2009. doi: 10.1109/TAC.2009.2014935
[42]	F. Padula and A. Visioli, “On the stabilizing PID controllers for integral processes,” IEEE Trans. Automat. Control, vol. 57, no. 2, pp. 494–499, Feb. 2012. doi: 10.1109/TAC.2011.2164821

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The Distribution of Zeros of Quasi-Polynomials

doi: 10.1109/JAS.2023.123597

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