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An improved stability criterion for a class of neutral differential equations. (English) Zbl 1163.34392
Summary: This work gives an improved criterion for asymptotical stability of a class of neutral differential equations. By introducing a new Lyapunov functional, we avoid the use of the stability assumption on the main operators and derive a novel stability criterion given in terms of a LMI, which is less restricted than that given by {\it J. H. Park} [Appl. Math. Lett. 17, 1203--1206 (2004; Zbl 1122.34339)] and {\it Y.G. Sun} and {\it L. Wang} [Appl. Math. Lett. 19, No. 9, 949--953 (2006; Zbl 1122.34340)].

##### MSC:
 34K40 Neutral functional-differential equations 34K20 Stability theory of functional-differential equations
Full Text:
##### References:
 [1] Agarwal, R. P.; Grace, S. R.: Asymptotic stability of certain neutral differential equations, Math. comput. Modelling 31, 9-15 (2000) · Zbl 1042.34569 · doi:10.1016/S0895-7177(00)00056-X [2] K. Gu, An integral inequality in the stability problem of time-delay system, in: 39th IEEE Conference on Decision and Control, Sydney, Australia, 2000, pp. 2805--2810 [3] Hale, J.; Lunel, S. M. Verduyn: Introduction to functional differential equations, (1993) · Zbl 0787.34002 [4] Park, J. H.: Delay-dependent criterion for asymptotic stability of a class of neutral equations, Appl. math. Lett. 17, 1203-1206 (2004) · Zbl 1122.34339 · doi:10.1016/j.aml.2003.05.013 [5] Sun, Y. G.; Wang, L.: Note on asymptotic stability of a class of neutral differential equations, Appl. math. Lett. 19, 949-953 (2006) · Zbl 1122.34340 · doi:10.1016/j.aml.2005.10.015