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All issues Volume 31 (2025) ESAIM: COCV, 31 (2025) 96 References
Open Access
Issue
ESAIM: COCV
Volume 31, 2025
Article Number 96
Number of page(s) 37
DOI https://doi.org/10.1051/cocv/2024055
Published online 05 December 2025
  1. R. Bellman and K.L. Cooke, Differential-Difference Equations. Academic Press, New York-London (1963). [Google Scholar]
  2. D. Breda, editor. Controlling delayed dynamics—advances in theory, methods and applications. Vol. 604 of CISM International Centre for Mechanical Sciences. Courses and Lectures. Springer, Cham (2023). [Google Scholar]
  3. C. Corduneanu, Y. Li and M. Mahdavi, Functional differential equations. Pure and Applied Mathematics (Hoboken). John Wiley & Sons, Inc., Hoboken, NJ (2016). [Google Scholar]
  4. O. Diekmann, S.A. van Gils, S.M. Verduyn Lunel and H.O. Walther, Delay equations: Functional-, complex-, and nonlinear analysis. Vol. 110 of Applied Mathematical Sciences. Springer-Verlag, New York (1995). [Google Scholar]
  5. R. Driver, Ordinary and Delay Differential Equations. Springer-Verlag, New York (1977). [Google Scholar]
  6. L.E. Els'golts' and S.B. Norkin, Introduction to the Theory and Application of the Theory of Differential Equations with Deviating Argument. Academic Press, New York (1973). [Google Scholar]
  7. K. Gu, V. Kharitonov and J. Chen, Stability of time-delay systems. Control Engineering. Birklmuser Boston, Inc., Boston, MA (2003). [Google Scholar]
  8. A. Halanay, Differential Equations: Stability, Oscillations, Time Lags. Academic Press, New York (1966). [Google Scholar]
  9. J.K. Hale and S.M. Verduyn Lunel, Introduction to functional-differential equations. Vol. 99 of Applied Mathematical Sciences. Springer-Verlag, New York (1993). [Google Scholar]
  10. T. Insperger and G. Stepân, Semi-discretization for time-delay systems. Vol. 178 of Applied Mathematical Sciences. Springer, New York (2011). [Google Scholar]
  11. V.B. Kolmanovskii and V.R. Nosov, Stability of Functional Differential Equations. Academic Press, New York (1986). [Google Scholar]
  12. N.N. Krasovskiï, Stability of Motion. Applications of Lyapunov's Second Method to Differential Systems and Equations with Delay. Stanford University Press, Stanford, Calif. (1963). [Google Scholar]
  13. G. Stâepâan, Retarded dynamical systems: stability and characteristic functions. Vol. 210 of Pitman Research Notes in Mathematics Series. Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York (1989). [Google Scholar]
  14. E. Witrant, E. Fridman, O. Sename and L. Dugard, editors. Recent results on time-delay systems. Analysis and control. Vol. 5 of Advances in Delays and Dynamics. Springer, Cham (2016). [Google Scholar]
  15. A. Halanay and J. Yorke, Some new results and problems in the theory of delay-differential equations. SIAM Rev. 13(1971) 55-80. [Google Scholar]
  16. G. Polya and G. Szegö, Problems and theorems in analysis. I. Classics in Mathematics. Springer-Verlag, Berlin (1998). [Google Scholar]
  17. I. Boussaada and S. Niculescu, Characterizing the codimension of zero singularities for time-delay systems. Acta A ppl. Math. 145(2016) 47-88. [Google Scholar]
  18. G. Mazanti, I. Boussaada and S.-I. Niculescu, Multiplicity-induced-dominancy for delay-differential equations of retarded type. J. Diff. Eq. 286 (2021) 84-118. [Google Scholar]
  19. E. Pinney, Ordinary Difference-Differential Equations. Univ. California Press (1958). [Google Scholar]
  20. I. Boussaada, I. Morarescu and S. Niculescu, Inverted pendulum stabilization: characterization of codimension-three triple zero bifurcation via multiple delayed proportional gains. Syst. Control Lett. 82 (2015) 1-9. [Google Scholar]
  21. A. Ramirez, S. Mondie, R. Garrido and R. Sipahi, Design of proportional-integral-retarded (PIR) controllers for second-order LTI systems. IEEE Trans. Automat. Control 61 (2016) 1688-1693. [Google Scholar]
  22. J. Sieber and B. Krauskopf, Bifurcation analysis of an inverted pendulum with delayed feedback control near a triple-zero eigenvalue singularity. Nonlinearity 17 (2004) 85-103. [Google Scholar]
  23. Y.I. Nehnark, The structure of the D-decomposition of the space of quasipolynomials and the diagrams of Vysnegradskiï and Nyquist. Doklady Akad. Nauk SSSR (N.S.) 60 (1948) 1503-1506. [Google Scholar]
  24. A. Benarab, I. Boussaada, S.-I. Niculescu and K. Trabelsi, Multiplicity-induced-dominancy for delay systems: Comprehensive examples in the scalar neutral case. Eur. J. Contr. (2023). [Google Scholar]
  25. I. Boussaada, G. Mazanti and S.-I. Niculescu, The generic multiplicity-induced-dominancy property from retarded to neutral delay-differential equations: when delay-systems characteristics meet the zeros of Kummer functions. C . R. Math. Acad. Sci. Paris 360 (2022) 349-369. [Google Scholar]
  26. H. Buchholz, The confluent hypergeometric function with special emphasis on its applications. Vol. 15 of Springer T racts in Natural Philosophy. Springer-Verlag (1969). [Google Scholar]
  27. A. Erdelyi, W. Magnus, F. Oberhettinger and F. Tricomi, Higher Transcendental Functions. Vol. I. Robert E. Krieger Publishing Co., Inc., Melbourne, Fla. (1981). [Google Scholar]
  28. M. Yoshida, Fuchsian Differential Equations. Springer (1987). [Google Scholar]
  29. I. Boussaada, G. Mazanti and S.-I. Niculescu, Pade approximation and hypergeometric functions: a missing link with the spectrum of delay-differential equations. IFAC-PapersOnLine 55 (2022) 206-211. [Google Scholar]
  30. I. Boussaada, G. Mazanti and S.-I. Niculescu, Some remarks on the location of non-asymptotic zeros of Whittaker and Kummer hypergeometric functions. Bull. Sci. Math. 174 (2022) Paper No. 103093. [Google Scholar]
  31. S.-I. Niculescu, I. Boussaada, X.-G. Li, G. Mazanti and C.-F. Mendez-Barrios, Stability, delays and multiple characteristic roots in dynamical systems: a guided tour. IFAC-PapersOnLine 54 (2021) 222-239. [Google Scholar]
  32. S. Fueyo, G. Mazanti, I. Boussaada, Y. Chitour and S.-I. Niculescu, On the pole placement of scalar linear delay systems with two delays. IMA J. Math. Control Inform. 40 (2023) 81-105. [Google Scholar]
  33. S. Niculescu, Delay effects on stability: a robust control approach. Vol. 269 of Lect. Notes Control. Inf. Sci. Springer-Verlag London Ltd., London (2001). [Google Scholar]
  34. R. Sipahi, S. Niculescu, C. Abdallah, W. Michiels and K. Gu, Stability and stabilization of systems with time delay: limitations and opportunities. IEEE Control Syst. Mag. 31 (2011) 38-65. [Google Scholar]
  35. I.H. Suh and Z. Bien, Proportional minus delay controller. IEEE Trans. Automatic Control 24 (1979) 370-372. [Google Scholar]
  36. I.H. Suh and Z. Bien, Use of time-delay actions in the controller design. IEEE Trans. Automatic Control 25 (1980) 600-603. [Google Scholar]
  37. C.T. Abdallah, P. Dorato, J. Benitez-Read and R. Byrne, Delayed positive feedback can stabilize oscillatory systems, in Proceedings of the 1993 American Control Conference. San Francisco, USA (1993) 3106-310. [Google Scholar]
  38. M.S. Lee and C.S. Hsu, On the τ-decomposition for stability analysis for retarded dynamical systems. SIAM J. Contr. 7 (1969) 242-259. [Google Scholar]
  39. W. Michiels and S. Niculescu, Stability, control, and computation for time-delay systems: an eigenvalue-based approach. Vol. 27 of Advances in Design and Control, 2nd edn. Soc. Ind. Appl. Math, Philadelphia, PA (2014). [Google Scholar]
  40. W. Michiels, K. Engelborghs, P. Vansevenant and D. Roose, The continuous pole placement method for delay equations. Automatica 38 (2002) 747-761. [Google Scholar]
  41. T. Balogh, I. Boussaada, T. Insperger and S.-I. Niculescu, Conditions for stabilizability of time-delay systems with real-rooted plant. Int. J. Robust Nonlinear Control 32 (2022) 3206-3224. [Google Scholar]
  42. I. Boussaada, G. Mazanti, S.-I. Niculescu and A. Benarab, MID property for delay systems: Insights on spectral values with intermediate multiplicity, in 61st IEEE Conference on Decision and Control (CDC 2022) (2022) 6881-6888. [Google Scholar]
  43. E. Hille. Oscillation theorems in the complex domain. Trans. Am. Math. Soc. 23 (1922) 350-385. [Google Scholar]
  44. F. Olver, D. Lozier, R. Boisvert and C. Clark, editors, NIST Handbook of Mathematical Functions. U.S. Department of Commerce, National Institute of Standards and Technology, Washington, DC; Cambridge University Press, Cambridge (2010). [Google Scholar]
  45. J. Auriol, I. Boussaada, R.J. Shor, H. Mounier and S.-I. Niculescu, Comparing advanced control strategies to eliminate stick-slip oscillations in drillstrings. IEEE Access 10 (2022) 10949-10969. [Google Scholar]
  46. J.J. Castillo-Zamora, I. Boussaada, A. Benarab and J. Escareno, Time-delay control of quadrotor unmanned aerial vehicles: a multiplicity-induced-dominancy-based approach. J. Vibr. Control 29 (2023) 2593-2608. [Google Scholar]
  47. C.A. Molnar, T. Balogh, I. Boussaada and T. Insperger, Calculation of the critical delay for the double inverted pendulum. J. Vibr. Control 27 (2020) 1-9. [Google Scholar]
  48. A. Benarab, I. Boussaada, K. Trabelsi and C. Bonnet, Multiplicity-induced-dominancy property for second-order neutral differential equations with application in oscillation damping. Eur. J. Control 69 (2023) Paper No. 100721. [Google Scholar]
  49. G. Mazanti, I. Boussaada, S.-I. Niculescu and Y. Chitour, Effects of roots of maximal multiplicity on the stability of some classes of delay differential-algebraic systems: The lossless propagation case, in Proceeding of 24th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2021). IFAC-PapersOnLine, Cambridge, United Kingdom (2021). [Google Scholar]
  50. I. Boussaada, S.-I. Niculescu, A. El-Ati, R Pâerez-Ramos and K Trabelsi, Multiplicity-induced-dominancy in parametric second-order delay differential equations: analysis and application in control design. ESAIM Control Optim. Calc. Var. 26 (2020) 34. [Google Scholar]
  51. D. Armbruster, D.E. Marthaler, C. Ringhofer, K. Kempf and T.-C. Jo, A continuum model for a re-entrant factory. O per. Res. 54 (2006) 933-950. [Google Scholar]
  52. J. Coron and S. Tamasoiu, Feedback stabilization for a scalar conservation law with PID boundary control. Chin. Ann. Math. B 36 (2015) 763-776. [Google Scholar]
  53. W. Michiels, I. Boussaada and S.-I. Niculescu, An explicit formula for the splitting of multiple eigenvalues for nonlinear eigenvalue problems and connections with the linearization for the delay eigenvalue problem. SIAM J. M atrix Anal. Applic. 38 (2017) 599-620. [Google Scholar]
  54. S.P. Bhattacharyya, H. Chapellat and L.H. Keel, Robust control: the parametric approach, in Advances in control e ducation 1994. Elsevier (1995) 49-52. [Google Scholar]
  55. A.P. Seyranian and A.A. Mailybaev, Multiparameter Stability Theory with Mechanical Applications, Vol. 13. World Scientific (2003). [Google Scholar]
  56. I. Boussaada, G. Mazanti, S. Niculescu and W. Michiels, Decay rate assignment through multiple spectral values in delay systems. Technical report, L2S (2023). [Google Scholar]
  57. J.S. Tripp, Development of a distributed parameter mathematical model for simulation of cryogenic wind tunnels. Technical Paper 2177, NASA (1983). [Google Scholar]
  58. E.S. Armstrong and J.S. Tripp, An application of multivariable design techniques to the control of the National Transonic Facility. Technical Paper 1887, NASA (1981). [Google Scholar]
  59. A.Z. Manitius, Feedback controllers for a wind tunnel model involving a delay: analytical design and numerical simulation. IEEE Trans. Automat. Control 29 (1984) 1058-1068. [Google Scholar]
  60. K. Engelborghs, M. Dambrine and D. Roose, Limitations of a class of stabilization methods for delay systems. IEEE Trans. Automatic Control 46 (2001) 336-339. [Google Scholar]
  61. S. Mondie and W. Michiels, Finite spectrum assignment of unstable time-delay systems with a safe implementation. IEEE Trans. Automatic Control 48 (2003) 2207-2212. [Google Scholar]
  62. T. Samad, A survey on industry impact and challenges thereof. IEEE Control Syst. Mag. 37 (2017) 17-18. [Google Scholar]
  63. D. Ma, I. Boussaada, J. Chen, C. Bonnet, S.-I. Niculescu and J. Chen, PID control design for first-order delay systems via MID pole placement: Performance vs. robustness. Automatica 137 (2022) 110102. [Google Scholar]
  64. I. Boussaada, G. Mazanti, S.-I. Niculescu, A. Hammoumou, T. Millet, J Raj and J Huynh, New features of P3<5 software. Insights and demos. IFAC-PapersOnLine 55 (2022) 246-251. [Google Scholar]
  65. I. Boussaada, G. Mazanti, S.-I. Niculescu, J. Huynh, F. Sim and M. Thomas. Partial pole placement via delay action: a Python software for delayed feedback stabilizing design, in 2020 24th International Conference on System T heory, Control and Computing (ICSTCC) (2020) 196-201. [Google Scholar]
  66. I. Boussaada, G. Mazanti, S.-I. Niculescu, A. Leclerc, J. Raj and M. Perraudin, New features of P3<5 software: partial pole placement via delay action. IFAC-PapersOnLine 54 (2021) 215-221. [Google Scholar]
  67. S. Amrane, F. Bedouhene, I. Boussaada and S.-I. Niculescu, On qualitative properties of low-degree quasipolynomi- als: further remarks on the spectral abscissa and rightmost-roots assignment. Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 61(2018) 361-381. [Google Scholar]
  68. F. Bedouhene, I. Boussaada and S.-I. Niculescu, Real spectral values coexistence and their effect on the stability of time-delay systems: Vandermonde matrices and exponential decay. C. R. Math. Acad. Sci. Paris 358 (2020) 1011-1032. [Google Scholar]
  69. K. Ammari, I. Boussaada, S.-I. Niculescu and S. Tliba, Multiplicity manifolds as an opening to prescribe exponential decay: auto-regressive boundary feedback in wave equation stabilization. preprint (2023). [Google Scholar]
  70. K. Ammari, I. Boussaada, S.-I. Niculescu, S. Tliba, Prescribing transport equation solution's decay via multiplicity manifold and autoregressive boundary control. Int. J. Robust. Nonlinear Control 34(2024) 6721-6740. [Google Scholar]

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