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On delay-dependent stability for linear neutral systems. (English) Zbl 1011.93062
Summary: This paper focuses on the problem of uniform asymptotic stability of a class of linear neutral systems. Sufficient conditions for delay-dependent stability are given in terms of the existence of solutions of some linear matrix inequalities. Furthermore, the proposed technique extends to neutral systems the results obtained for delay-difference equations using model transformations. Illustrative examples are included.

93C23Systems governed by functional-differential equations
34K40Neutral functional-differential equations
15A39Linear inequalities of matrices
93D20Asymptotic stability of control systems
Full Text: DOI
[1] Bellen, A.; Guglielmi, N.; Ruehli, A. E.: Methods for linear systems of circuits delay differential equations of neutral type. IEEE transactions on circuits and systems 46, 212-216 (1999) · Zbl 0952.94015
[2] Chen, J.: On computing the maximal delay intervals for stability of linear delay systems. IEEE transactions on automatic control 40, 1087-1093 (1995) · Zbl 0840.93074
[3] Chen, J., & Latchman, H. A. (1994). Asymptotic stability independent of delays: Simple necessary and sufficient conditions. Proceedings of American control conference, Baltimore, USA (pp. 1027-1031).
[4] Gu, K.; Niculescu, S. -I.: Additional eigenvalues in transformed time-delay systems. IEEE transactions on automatic control 45, 572-576 (2000) · Zbl 0986.34066
[5] Hale, J. K.; Lunel, S. M. Verduyn: Introduction to functional differential equations. Applied mathematical sciences 99 (1993) · Zbl 0787.34002
[6] Huang, Y. P.; Zhou, K.: Robust stability of uncertain time-delay systems. IEEE transactions on automatic control 45, 2169-2173 (2000) · Zbl 0989.93066
[7] Kolmanovskii, V. B.: The stability of hereditary systems of neutral type. Journal of applied mathematics and mechanics 60, 205-216 (1996)
[8] Kolmanovskii, V. B.; Myshkis, A. D.: Applied theory of functional differential equations. (1992) · Zbl 0917.34001
[9] Kolmanovskii, V. B., Richard, J.-P., & Tchangani, A. Ph. (1998). Stability of linear systems with discrete-plus-distributed delays: Application to some model transformations. Proceedings of MTNS’98, Padova, Italy.
[10] Li, X. (1997). Robust stabilization and H\infty control of time-delay systems. Ph.D. Thesis, University of Newcastle, Australia, October 1997.
[11] Lien, C. -H.; Yu, K. -W.; Hsieh, J. -G.: Stability conditions for a class of neutral systems with multiple time delay systems. Journal of mathematical analysis and applications 245, 20-27 (2000) · Zbl 0973.34066
[12] Niculescu, S. I.; Brogliato, B.: Force measurements time-delays and contact instability phenomenon. European journal of control 5, 279-289 (1999) · Zbl 0936.93031
[13] Niculescu, S.-I., Verriest, E. I., Dugard, L., & Dion, J.-M. (1998). Stability and robust stability of time-delay systems: A guided tour. In L. Dugard & E. I. Verriest (Eds.), Stability and control of time-delay systems, Vol. 228 (pp. 1-71) London: LNCIS, Springer. · Zbl 0914.93002
[14] Park, P.: A delay dependent stability criterion for systems with uncertain time-invariant delays. IEEE transactions on automatic control 44, 876-878 (1999) · Zbl 0957.34069
[15] Richard, J. P., Goubet-Bartholomeus, A., Tchangani, P. A., & Dambrine, M. (1998). Nonlinear delay systems: Tools for a quantitative approach to stabilization. In L. Dugard & E. I. Verriest (Eds.), Stability and control of time-delay systems. London: LNCIS, Springer. · Zbl 0918.93041
[16] Verriest, E. I.: Robust stability of deterministic and stochastic time delay systems. Journal européen des systèmes automatisés (JESA) 31, 1013-1024 (1997)
[17] Verriest, E. I. (1998). Robust stability of differential-delay systems. Zeitschrift für Angewandte Mathematik und Mechanik (pp. S1107-S1108). · Zbl 0925.34104
[18] Verriest, E. I., & Niculescu, S.-I. (1998). Delay-independent stability of linear neutral systems: A Riccati equation approach. In L. Dugard & E. I. Verriest (Eds.), Stability and control of time-delay systems. London: LNCIS, Springer (Chapter 3). · Zbl 0923.93049