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Stability criterion for neutral differential systems with mixed multiple time-varying delay arguments. (English) Zbl 1006.34072

Summary: Here, the asymptotic stability for neutral delay-differential systems with mixed multiple time-varying delay arguments is investigated. Based on the Lyapunov method, two new stability criteria in terms of linear matrix inequalities (LMIs) are presented to guarantee the stability for the systems. The LMIs can be easily solved by various convex optimization algorithms. Three numerical examples are given to illustrate the proposed methods.

MSC:

34K20 Stability theory of functional-differential equations
34K40 Neutral functional-differential equations

Software:

LMI toolbox
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Full Text: DOI

References:

[1] B. Boyd, L.E. Ghaoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory, Philadelphia, SIAM, 1994.; B. Boyd, L.E. Ghaoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory, Philadelphia, SIAM, 1994. · Zbl 0816.93004
[2] Brayton, R. K.; Willoughby, R. A., On the numerical integration of a symmetric system of difference-differential equations of neutral type, J. Math. Anal. Applications, 18, 182-189 (1967) · Zbl 0155.47302
[3] Chen, W., Comment on simple criteria for stability of neutral systems with multiple delays, Int. J. Syst. Sci., 30, 1247-1248 (1999) · Zbl 1023.93053
[4] P. Gahinet, A. Nemirovski, A. Laub, M. Chilali, LMI Control Toolbox User’s Guide, The Mathworks, Natick, MA, 1995.; P. Gahinet, A. Nemirovski, A. Laub, M. Chilali, LMI Control Toolbox User’s Guide, The Mathworks, Natick, MA, 1995.
[5] K. Gopalsamy, Stability and Oscillations in Delay Differential Equations of Population Dynamics, Kluwer Academic Publishers, Boston, 1992.; K. Gopalsamy, Stability and Oscillations in Delay Differential Equations of Population Dynamics, Kluwer Academic Publishers, Boston, 1992. · Zbl 0752.34039
[6] Hale, J.; Infante, E. F.; Tsen, F. P., Stability in linear delay equations, J. Math. Anal. Applications, 105, 533-555 (1985) · Zbl 0569.34061
[7] J. Hale, S.M. Verduyn Lunel, Introduction to Functional Differential Equations, Springer, New York, 1993.; J. Hale, S.M. Verduyn Lunel, Introduction to Functional Differential Equations, Springer, New York, 1993. · Zbl 0787.34002
[8] Hu, G. D.; Hu, G. D., Some simple stability criteria of neutral delay-differential systems, Appl. Math. Comput., 80, 257-271 (1996) · Zbl 0878.34063
[9] G.D. Hui, G.D. Hu, Simple criteria for stability of neutral systems with multiple delays, Int. J. Syst. Sci., 28 (1997), 1325-1328.; G.D. Hui, G.D. Hu, Simple criteria for stability of neutral systems with multiple delays, Int. J. Syst. Sci., 28 (1997), 1325-1328. · Zbl 0899.93031
[10] Khusainov, D. Y.; Yun’Kova, E. V., Investigation of the stability of linear systems of neutral type by the Lyapunov function method, Differentsialnye Uravneniya, 24, 613-621 (1988)
[11] V. Kolmanovskii, A. Myshkis, Applied Theory of Functional Differential Equations, Kluwer Academic Publishers, Dordrecht, 1992.; V. Kolmanovskii, A. Myshkis, Applied Theory of Functional Differential Equations, Kluwer Academic Publishers, Dordrecht, 1992. · Zbl 0917.34001
[12] Kuang, J. X.; Xiang, J. X.; Tian, H. J., The asymptotic stability of one-parameter methods for neutral differential equations, BIT, 34, 400-408 (1994) · Zbl 0814.65078
[13] Li, L. M., Stability of linear neutral delay-differential systems, Bull. Aust. Math. Soc., 38, 339-344 (1988) · Zbl 0669.34074
[14] Y.S. Moon, Robust Control of Time-Delay System using Linear Matrix Inequalities, Ph.D. Thesis, Seoul National University, South Korea, 1998.; Y.S. Moon, Robust Control of Time-Delay System using Linear Matrix Inequalities, Ph.D. Thesis, Seoul National University, South Korea, 1998.
[15] Park, J. H.; Won, S., A note on stability of neutral delay-differential systems, J. Franklin Inst., 336, 543-548 (1999) · Zbl 0969.34066
[16] Park, J. H.; Won, S., Asymptotic stability of neutral systems with multiple delays, J. Optimizat. Theory Applications, 103, 187-200 (1999) · Zbl 0947.65088
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