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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.

MSC:
93C23 Control/observation systems governed by functional-differential equations
34K40 Neutral functional-differential equations
15A39 Linear inequalities of matrices
93D20 Asymptotic stability in control theory
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[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.; Verduyn Lunel, S.M., Introduction to functional differential equations, Applied mathematical sciences, Vol. 99, (1993), Springer New York · 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) · Zbl 0880.34079
[8] Kolmanovskii, V.B.; Myshkis, A.D., Applied theory of functional differential equations, (1992), Kluwer Dordrecht, The Netherlands · Zbl 0907.39012
[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∞ 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).
[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
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