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Asymptotic stability of neutral systems with multiple delays. (English) Zbl 0947.65088
Summary: The stability analysis problem for linear neutral delay-differential systems with multiple time delays is investigated. Using the Lyapunov method, we present new sufficient conditions for the asymptotic stability of systems in terms of linear matrix inequalities, which can be solved easily by various convex optimization algorithms. Numerical examples are given to illustrate the application of the proposed method.

MSC:
65L07 Numerical investigation of stability of solutions to ordinary differential equations
90C25 Convex programming
34K20 Stability theory of functional-differential equations
34K40 Neutral functional-differential equations
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[1] Kolmanovskii, V., and Myshkis, A., Applied Theory of Functional Differential Equations, Kluwer Academic Publishers, Dordrecht, Holland, 1992. · Zbl 0917.34001
[2] Hale, J., and Verduyn Lunel, S. M., Introduction to Functional Differential Equations, Springer Verlag, New York, New York, 1993. · Zbl 0787.34002
[3] Gopalsamy, K., Stability and Oscillations in Delay Differential Equations of Population Dynamics, Kluwer Academic Publishers, Boston, Massachusetts, 1992. · Zbl 0752.34039
[4] Kuang, J. X., Xiang, J. X., and Tian, H. J., The Asymptotic Stability of One-Parameter Methods for Neutral Differential Equations, BIT, Vol. 34, pp. 400–408, 1994. · Zbl 0814.65078
[5] Li, L. M., Stability of Linear Neutral Delay-Differential Systems, Bulletin of the Australian Mathematical Society, Vol. 38, pp. 339–344, 1988. · Zbl 0669.34074
[6] Hui, G. D., and Hu, G. D., Some Simple Stability Criteria of Neutral Delay-Differential Systems, Applied Mathematics and Computation, Vol. 80, pp. 257–271, 1996. · Zbl 0878.34063
[7] Brayton, R. K., and Willoughby, R. A., On the Numerical Integration of a Symmetric System of Difference-Differential Equations of Neutral Type, Journal of Mathematical Analysis and Applications, Vol. 18, pp. 182–189, 1967. · Zbl 0155.47302
[8] Khusainov, D. Ya, and Yunkova, E. V., Investigation of the Stability of Linear Systems of Neutral Type by the Lyapunov Function Method, Differentsialnye Uravneniya, Vol. 24, pp. 613–621, 1988.
[9] Hale, J. K., Infante, E. F., and Tsen, F. S. P., Stability of Linear Delay Equations, Journal of Mathematical Analysis and Applications, Vol. 105, pp. 533–555, 1985. · Zbl 0569.34061
[10] Hui, G. D. and Hu, G. D., Simple Criteria for Stability of Neutral Systems with Multiple Delays, International Journal of Systems Science, Vol. 28, pp. 1325–1328, 1997. · Zbl 0899.93031
[11] Boyd, S., El Ghaoui, L., Feron, E., and Balakrishnan, V., Linear Matrix Inequalities in Systems and Control Theory, Studies in Applied Mathematics, SIAM, Philadelphia, Pennsylvania, Vol. 15, 1994. · Zbl 0816.93004
[12] Khargonekar, P. P., Petersen, I. R., and Zhou, K., Robust Stabilization of Uncertain Linear Systems: Quadratic Stability and HControl Theory, IEEE Transactions on Automatic Control, Vol. 35, pp. 356–361, 1990. · Zbl 0707.93060
[13] Alvert, A., Conditions for Positive and Nonnegative Definiteness in Terms of Pseudoinverses, SIAM Journal on Applied Mathematics, Vol. 17, pp. 434–440, 1969. · Zbl 0265.15002
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