On robust stability of neutral systems

Silviu-Iulian Niculescu

Kybernetika (2001)

  • Volume: 37, Issue: 3, page [253]-263
  • ISSN: 0023-5954

Abstract

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This paper focuses on the problem of uniform asymptotic stability of a class of linear neutral systems including some constant delays and time-varying cone-bounded nonlinearities. Sufficient stability conditions are derived by taking into account the weighting factors describing the nonlinearities. The proposed results are applied to the stability analysis of a class of lossless transmission line models.

How to cite

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Niculescu, Silviu-Iulian. "On robust stability of neutral systems." Kybernetika 37.3 (2001): [253]-263. <http://eudml.org/doc/33533>.

@article{Niculescu2001,
abstract = {This paper focuses on the problem of uniform asymptotic stability of a class of linear neutral systems including some constant delays and time-varying cone-bounded nonlinearities. Sufficient stability conditions are derived by taking into account the weighting factors describing the nonlinearities. The proposed results are applied to the stability analysis of a class of lossless transmission line models.},
author = {Niculescu, Silviu-Iulian},
journal = {Kybernetika},
keywords = {asymptotic stability; linear neutral system; asymptotic stability; linear neutral system},
language = {eng},
number = {3},
pages = {[253]-263},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On robust stability of neutral systems},
url = {http://eudml.org/doc/33533},
volume = {37},
year = {2001},
}

TY - JOUR
AU - Niculescu, Silviu-Iulian
TI - On robust stability of neutral systems
JO - Kybernetika
PY - 2001
PB - Institute of Information Theory and Automation AS CR
VL - 37
IS - 3
SP - [253]
EP - 263
AB - This paper focuses on the problem of uniform asymptotic stability of a class of linear neutral systems including some constant delays and time-varying cone-bounded nonlinearities. Sufficient stability conditions are derived by taking into account the weighting factors describing the nonlinearities. The proposed results are applied to the stability analysis of a class of lossless transmission line models.
LA - eng
KW - asymptotic stability; linear neutral system; asymptotic stability; linear neutral system
UR - http://eudml.org/doc/33533
ER -

References

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  1. Abolinia V. E., Myshkis A. D., Mixed problem for an almost linear hyperbolic system in the plane (in Russian), Mat. Sb. 12 (1960), 423–442 (1960) 
  2. Boyd S., Ghaoui L. El, Feron, E., Balakrishnan V., Linear matrix inequalities in system and control theory, SIAM Stud. Appl. Math. 15 (1994) (1994) Zbl0816.93004MR1284712
  3. Brayton R. K., Nonlinear oscillations in a distributed network, Quart. Appl. Math. 24 (1976), 289–301 (1976) 
  4. Brayton R. K., Miranker W. L., Oscillations in a distributed network, Arch. Rational Mech. Anal. 17 (1964), 358–376 (1964) MR0168864
  5. Chen J., 10.1109/9.388690, IEEE Trans. Automat. Control 40 (1995), 1087–1093 (1995) Zbl0840.93074MR1345968DOI10.1109/9.388690
  6. Cooke K. L., Krumme D. W., 10.1016/0022-247X(68)90038-3, J. Math. Anal. Appl. 24 (1968), 372–387 (1968) MR0232089DOI10.1016/0022-247X(68)90038-3
  7. Ghaoui L. El, Niculescu S.-I., Robust decision problems in engineering: An LMI approach, In: Advances in Linear Matrix Inequality Method in Control, SIAM, Philadelphia, 1999 MR1736563
  8. Els’golts’ L. E., Norkin S. B., Introduction to the Theory and Application of Differential Equations with Deviating Arguments (Math, Sci. Engrg. 105). Academic Press, New York 1973 MR0352647
  9. Halanay A., Răsvan, Vl., 10.1093/imamci/14.1.95, IMA J. Math. Control Inform. 14 (1997) 95–107 (1997) Zbl0873.93067MR1446966DOI10.1093/imamci/14.1.95
  10. Hale J. K., Lunel S. M. Verduyn, Introduction to Functional Differential Equations (Appl, Math. Sci. 99). Springer–Verlag, New York 1993 MR1243878
  11. Hale J. K., Infante E. F., Tseng F. S. P., 10.1016/0022-247X(85)90068-X, J. Math. Anal. Appl. 105 (1985), 533–555 (1985) MR0778486DOI10.1016/0022-247X(85)90068-X
  12. Kolmanovskii V. B., Myshkis A., Applied Theory of Functional Differential Equations, Kluwer, Dordrecht 1992 MR1256486
  13. Lakshmikantam V., Leela S., Differential and integral inequalities, Volume II. Academic Press, New York 1969 
  14. Malek–Zavarei M., Jamshidi M., Time Delay Systems: Analysis, Optimization and Applications (Systems and Control Series 9), North–Holland, Amsterdam 1987 MR0930450
  15. Niculescu S.-I., Time-delay Systems, Qualitative Aspects on Stability and Stabilization (in French). Diderot Eds. Paris, ‘Nouveaux Essais’ Series, Paris 1997 Zbl1235.93006
  16. Niculescu S.-I., Brogliato B., On force measurements time-delays in control of constrained manipulators, In: Proc. IFAC on System Structure and Control, Nantes 1995, pp. 266–271 (1995) 
  17. Niculescu S.-I., Verriest E. I., Dugard, L., Dion J.-M., Stability and robust stability of time-delay systems: A guided tour, In: Stability and Control of Time-delay Systems (L. Dugard and E. I. Verriest, eds., Lecture Notes on Control and Information Sciences 228), Springer–Verlag, London 1998 Zbl0914.93002MR1482571
  18. Răsvan, Vl., Absolute Stability of Time Lag Control Systems (in Romanian), Ed. Academiei, Bucharest 1975 (Russian revised edition by Nauka, Moscow, 1983) (1975) MR0453048
  19. Răsvan, Vl., Dynamical systems with lossless propagation and neutral functional differential equations, In: Proc. MTNS’98, Padoue 1998, pp. 527–531 (1998) 
  20. Slemrod M., Infante E. F., 10.1016/0022-247X(72)90098-4, J. Math. Anal. Appl. 38 (1972), 399–415 (1972) MR0306678DOI10.1016/0022-247X(72)90098-4
  21. Verriest E. I., Fan M. K. H., Kullstam J., Frequency domain robust stability criteria for linear delay systems, In: Proc. 32nd IEEE Conference on Decision and Control, San Antonio 1993, pp. 3473–3478 (1993) 
  22. Verriest E. I., Riccati type conditions for robust stability of delay systems (preprint), Presented at MTNS’96, St. Louis 1996 
  23. Verriest E. I., Robust stability of time-varying systems with unknown bounded delays, In: Proc. 33rd IEEE Conference on Decision and Control, Lake Buena Vista 1994, pp. 417–422 (1994) 
  24. Verriest E. I., Niculescu S.-I., Delay-independent stability of linear neutral systems: A Riccati equation approach, In: Stability and Control of Time-delay Systems (L. Dugard and E. I. Verriest, eds., Lecture Notes on Control and Information Sciences 228), Springer–Verlag, London 1998 Zbl0923.93049MR1482573

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