Stability of neutral systems with commensurate delays and poles asymptotic to the imaginary axis

SIAM Journal on Control and Optimization

Volumn 49, Issue 2, 2011, Pages 498-516

  Bonnet, Catherine ^a   Fioravanti, André R ^a   Partington, Jonathan R ^b  

^a SUPELEC   (France)

^b UNIVERSITY OF LEEDS   (United Kingdom)

Author keywords

Delay effects; H stability; H stabilizability; Neutral systems

Indexed keywords

DELAY CONTROL SYSTEMS; POLES;

COMMENSURATE DELAYS; DELAY EFFECTS; IMAGINARY AXIS; NEUTRAL SYSTEMS; NEUTRAL TIME DELAY SYSTEMS; STABILITY ANALYSIS; STABILIZABILITY;

SYSTEM STABILITY;

EID: 79957440944     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/090776275     Document Type: Article

References (25)

1. C.E. Avelar and J.K. Hale, On the zeros of exponential polynomials, J. Math. Anal. Appl., 73 (1980), pp. 434-452.
2. R. Bellman and K.L. Cooke, Differential-Difference Equations, Academic Press, New York, London, 1963.
3. D. Breda, S. Maset, and R. Vermiglio, Computing the characteristic roots for delay differential equations, IMA J. Numer. Anal., 24 (2004), pp. 1-19. (Pubitemid 38118627)
4. C. Bonnet and J.R. Partington, Bézout factors and L1-optimal controllers for delay systems using a two-parameter compensator scheme, IEEE Trans. Automat. Control, 44 (1999), pp. 1512-1521. (Pubitemid 30508556)
5. K. Engelborghs, T. Luzyanina, and D. Roose, Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL, ACM Trans. Math. Software, 28 (2002), pp. 1-21. (Pubitemid 135686769)
6. A.R. Fioravanti, C. Bonnet, H. Özbay, and S.-I. Niculescu, A numerical method to find stability windows and unstable poles for linear neutral time-delay systems, in Proceedings of the IFACWorkshop on Time-Delay Systems (TDS'10, Prague), Czech Technical University, Prague, 2010.
7. T.T. Georgiou and M.C. Smith, w-stability of feedback systems, Systems Control Lett., 13 (1989), pp. 271-277.
8. J.K. Hale and S.M. Verduyn Lunel, Introduction to Functional Differential Equations, Springer-Verlag, New York, 1993.
9. J.K. Hale and S.M. Verduyn Lunel, Strong stabilization of neutral functional differential equations, IMA J. Math. Control Inform., 19 (2002), pp. 5-23. (Pubitemid 34459987)
10. O.L.R. Jacobs, Introduction to Control Theory, Oxford University Press, Oxford, UK, 1974.
11. J.J. Loiseau, M. Cardelli, and X. Dusser, Neutral-type time-delay systems that are not formally stable are not BIBO stabilizable, IMA J. Math. Control Inform., 19 (2002), pp. 217-227. (Pubitemid 34460001)
12. W. Michiels and T. Vyhlídal, An eigenvalue based approach to the stabilization of time-delay systems of neutral type, Automatica J. IFAC, 41 (2005), pp. 991-998. (Pubitemid 40556808)
13. W. Michiels, T. Vhylídal, P. Zítek, H. Nijmeijer, and D. Henrion, Strong stability of neutral equations with an arbitrary delay dependency structure, SIAM J. Control Optim., 48 (2009), pp. 763-786.
14. S.I. Niculescu and K. Gu, Advances in Time-Delay Systems, Springer-Verlag, New York, 2004.
15. D.A. O'Connor and T.J. Tarn, On stabilization by state feedback for neutral differentialdifference equations, IEEE Trans. Automat. Control, 28 (1983), pp. 615-618. (Pubitemid 13556039)
16. L. Pandolfi, Stabilization of neutral functional differential equations, J. Optim. Theory Appl., 20 (1976), pp. 191-204.
17. J.R. Partington, Approximation of unstable infinite-dimensional systems using coprime factors, Systems Control Lett., 16 (1991), pp. 89-96.
18. J.R. Partington and C. Bonnet, H∞ and BIBO stabilization of delay systems of neutral type, Systems Control Lett., 52 (2004), pp. 283-288.
19. L.S. Pontryagin, On the zeros of some elementary transcendental functions, Amer. Math. Soc. Transl., 2 (1955), pp. 95-110.
20. R. Rabah, G.M. Sklyar, and A.V. Rezounenko, On strong regular stabilizability for linear neutral type systems, J. Differential Equations, 245 (2008), pp. 569-593.
21. R. Rabah, G.M. Sklyar, and A.V. Rezounenko, Stability analysis of neutral type systems in Hilbert space, J. Differential Equations, 214 (2005), pp. 391-428. (Pubitemid 40621909)
22. J.P. Richard, Time-delay systems: An overview of some recent advances and open problems, Automatica J. IFAC, 39 (2003), pp. 1667-1694.
23. M.C. Smith, On stabilization and the existence of coprime factorizations, IEEE Trans. Automat. Control, 34 (1989), pp. 1005-1007.
24. T. Vyhlídal and P. Zítek, Quasipolynomial mapping based rootfinder for analysis of time delay systems, in Proceedings of the IFAC Workshop on Time-Delay Systems (TDS'03, Rocquencourt), Rocquencourt, France, 2003.
25. K. Walton and J.E. Marshall, Direct method for TDS stability analysis, IEE Proceedings D, 134 (1987), pp. 101-107. (Pubitemid 17554365)