Geodesic
Stability Criteria of Linear Neutral Systems With Distributed Delays
Kybernetika, Tome 47 (2011) no. 2, pp. 273-284 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this paper, stability of linear neutral systems with distributed delay is investigated. A bounded half circular region which includes all unstable characteristic roots, is obtained. Using the argument principle, stability criteria are derived which are necessary and sufficient conditions for asymptotic stability of the neutral systems. The stability criteria need only to evaluate the characteristic function on a straight segment on the imaginary axis and the argument on the boundary of a bounded half circular region. If there are no characteristic roots on the imaginary axis, the number of unstable characteristic roots can be obtained. The results of this paper extend those in the literature. Numerical examples are given to illustrate the presented results.
In this paper, stability of linear neutral systems with distributed delay is investigated. A bounded half circular region which includes all unstable characteristic roots, is obtained. Using the argument principle, stability criteria are derived which are necessary and sufficient conditions for asymptotic stability of the neutral systems. The stability criteria need only to evaluate the characteristic function on a straight segment on the imaginary axis and the argument on the boundary of a bounded half circular region. If there are no characteristic roots on the imaginary axis, the number of unstable characteristic roots can be obtained. The results of this paper extend those in the literature. Numerical examples are given to illustrate the presented results.
Classification : 34K06, 65L07
Keywords: neutral systems; distributed delay; stability criteria 
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Hu, Guang-Da. Stability Criteria of Linear Neutral Systems With Distributed Delays. Kybernetika, Tome 47 (2011) no. 2, pp. 273-284. http://geodesic.mathdoc.fr/item/KYB_2011_47_2_a6/

[1] Brown, J. W., Churchill, R. V.: Complex Variables and Applications. McGraw–Hill Companies, Inc. and China Machine Press, Beijing 2004. | MR

[2] Hale, J. K., Lunel, S. M. Verduyn: Introdution to Functional Equations. Springer–Verlag, New York 1993.

[3] Hale, J. K., Lunel, S. M. Verduyn: Strong stabilization of neutral functional differential equations. IMA J. Math. Control Inform. 19 (2002), 5–23. | DOI | MR

[4] Hu, G. Da, Hu, G. Di: Stability of neutral-delay differential systems: boundary criteria. Appl. Math. Comput. 87 (1997), 247–259. | DOI | MR | Zbl

[5] Hu, G. Da, Liu, M.: Stability criteria of linear neutral systems with multiple delays. IEEE Trans. Automat. Control 52 (2007), 720–724. | DOI | MR

[6] Hu, G. Da, Mitsui, T.: Stability analysis of numerical methods for systems of neutral delay-differential equations. BIT 35 (1995), 504–515. | DOI | MR | Zbl

[7] Kolmanovskii, V. B., Myshkis, A.: Applied Theory of Functional Differential Equations. Kluwer Academic Publishers, Dordrecht 1992. | MR

[8] Lancaster, P.: The Theory of Matrices with Applications. Academic Press, Orlando 1985. | MR

[9] Li, H., Zhong, S., Li, H.: Some new simple stability criteria of linear neutral systems with a single delay. J. Comput. Appl. Math. 200 (2007), 441–447. | DOI | MR | Zbl

[10] Michiels, W., Niculescu, S.: Stability and Stabilization of Time Delay Systems: An Eigenvalue Based Approach. SIAM, Philadelphia 2007. | MR | Zbl

[11] Park, J. H.: A new delay-dependent stability criterion for neutral systems with multiple delays. J. Comput. Appl. Math. 136 (2001), 177–184. | DOI | MR

[12] Vyhlídal, T., Zítek, P.: Modification of Mikhaylov criterion for nuetral time-delay systems. IEEE Trans. Automat. Control 54 (2009), 2430–2435. | DOI | MR