Previous |  Up |  Next


neutral systems; distributed delay; stability criteria
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.
[1] Brown, J. W., Churchill, R. V.: Complex Variables and Applications. McGraw–Hill Companies, Inc. and China Machine Press, Beijing 2004. MR 0730937
[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 10.1093/imamci/19.1_and_2.5 | MR 1899001
[4] Hu, G. Da, Hu, G. Di: Stability of neutral-delay differential systems: boundary criteria. Appl. Math. Comput. 87 (1997), 247–259. DOI 10.1016/S0096-3003(96)00300-1 | MR 1468302 | Zbl 0913.34060
[5] Hu, G. Da, Liu, M.: Stability criteria of linear neutral systems with multiple delays. IEEE Trans. Automat. Control 52 (2007), 720–724. DOI 10.1109/TAC.2007.894539 | MR 2310053
[6] Hu, G. Da, Mitsui, T.: Stability analysis of numerical methods for systems of neutral delay-differential equations. BIT 35 (1995), 504–515. DOI 10.1007/BF01739823 | MR 1431345 | Zbl 0841.65062
[7] Kolmanovskii, V. B., Myshkis, A.: Applied Theory of Functional Differential Equations. Kluwer Academic Publishers, Dordrecht 1992. MR 1256486
[8] Lancaster, P.: The Theory of Matrices with Applications. Academic Press, Orlando 1985. MR 0245579
[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 10.1016/ | MR 2276843 | Zbl 1112.34058
[10] Michiels, W., Niculescu, S.: Stability and Stabilization of Time Delay Systems: An Eigenvalue Based Approach. SIAM, Philadelphia 2007. MR 2384531 | Zbl 1140.93026
[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 10.1016/S0377-0427(00)00583-5 | MR 1855889
[12] Vyhlídal, T., Zítek, P.: Modification of Mikhaylov criterion for nuetral time-delay systems. IEEE Trans. Automat. Control 54 (2009), 2430–2435. DOI 10.1109/TAC.2009.2029301 | MR 2562848
Partner of
EuDML logo