On the exponential stability of a neutral differential equation of first order

• Autorzy: Gözen M. , Tunç C.

Identyfikatory

DOI

10.7862/rf.2018.8

• Języki publikacji: EN

Abstrakty

EN

In this work, we establish some assumptions that guaranteeing the global exponential stability (GES) of the zero solution of a neutral differential equation (NDE). We aim to extend and improves some results found in the literature.

Słowa kluczowe

EN

GES; global exponential stability; NDE; neutral differential equation; time-varying delays

PL

GES; globalna stabilność wykładnicza; NDE; równanie różniczkowe neutralne; opóźnienia zmienne w czasie

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2018
• Tom: Vol. 41
• Strony: 95--107
• Opis fizyczny: Bibliogr. 25 poz.

Twórcy

autor

Gözen M.

• Department of Business Administration, Management Faculty, Van Yuzuncu Yil University, 65080, Erciş, Turkey

autor

Tunç C.

• Department of Mathematics Faculty of Sciences, Van Yuzuncu Yil University, 65080, Van Turkey

Bibliografia

• [1] R.P. Agarwal, S.R. Grace, Asymptotic stability of certain neutral differential equations, Math. Comput. Modelling 31 (8-9) (2000) 9-15.
• [2] H. Chen, X. Meng, An improved exponential stability criterion for a class of neutral delayed differential equations, Appl. Math. Lett. 24 (11) (2011) 1763-1767.
• [3] H. Chen, Some improved criteria exponential stability of neutral differential equation, Adv. Difference Equ. 2012 (2012:170) 9 pp.
• [4] S. Deng, X. Liao, S. Guo, Asymptotic stability analysis of certain neutral differential equations: a descriptor system approach, Math. Comput. Simulation 79 (10) (2009) 2981-2993.
• [5] H.A. El-Morshedy, K. Gopalsamy, Non-oscillation, oscillation and convergence of a class of neutral equations. Lakshmikantham's legacy: a tribute on his 75th birthday, Nonlinear Anal. 40 (1-8) (2000) Ser. A: Theory Methods 173-183.
• [6] E. Fridman, New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems, Systems Control Lett. 43 (4) (2001) 309-319.
• [7] M.R.S. Kulenovic, G. Ladas, A. Meimaridou, Necessary and sufficient condition for oscillations of neutral differential equations, J. Austral. Math. Soc. Ser. B 28 (3) (1987) 362-375.
• [8] O.M. Kwon, Ju H. Park, On improved delay-dependent stability criterion of certain neutral differential equations, Appl. Math. Comput. 199 (1) (2008) 385-391.
• [9] X. Li, Global exponential stability for a class of neural networks, Appl. Math. Lett. 22 (8) (2009) 1235-1239.
• [10] P.T. Nam, V.N. Phat, An improved stability criterion for a class of neutral differential equations, Appl. Math. Lett. 22 (1) (2009) 31-35.
• [11] Ju H. Park, S. Won, Stability analysis for neutral delay-differential systems, J. Franklin Inst. 337 (1) (2000) 1-9.
• [12] Ju H. Park, Ho Y. Jung, On the exponential stability of a class of nonlinear systems including delayed perturbations, J. Comput. Appl. Math. 159 (2) (2003) 467-471.
• [13] J.H. Park, Delay-dependent criterion for asymptotic stability of a class of neutral equations, Appl. Math. Lett. 17 (10) (2004) 1203-1206.
• [14] Ju H. Park, O. Kwon, On new stability criterion for delay-differential systems of neutral type, Appl. Math. Comput. 162 (2) (2005) 627-637.
• [15] Ju H. Park, O.M. Kwon, Stability analysis of certain nonlinear differential equation, Chaos Solitons Fractals 37 (2) (2008) 450-453.
• [16] T. Rojsiraphisal, P. Niamsup, Exponential stability of certain neutral differential equations, Appl. Math. Comput. 217 (8) (2010) 3875-3880.
• [17] Y.G. Sun, L. Wang, Note on asymptotic stability of a class of neutral differential equations, Appl. Math. Lett. 19 (9) (2006) 949-953.
• [18] C. Tunç, Asymptotic stability of nonlinear neutral differential equations with constant delays: a descriptor system approach, Ann. Differential Equations 27 (1) (2011) 1-8.
• [19] C. Tunç, Exponential stability to a neutral differential equation of first order with delay, Ann. Differential Equations 29 (3) (2013) 253-256.
• [20] C. Tunç, Asymptotic stability of solutions of a class of neutral differential equations with multiple deviating arguments, Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 57 (105) (1) (2014) 121-130.
• [21] C. Tunç, On the uniform asymptotic stability to certain first order neutral differential equations, Cubo 16 (2) (2014) 111-119.
• [22] C. Tunç, Convergence of solutions of nonlinear neutral differential equations with multiple delays, Bol. Soc. Mat. Mex. 21 (2) (2015) 219-231.
• [23] C. Tunç, Y. Altun, Asymptotic stability in neutral differential equations with multiple delays, J. Math. Anal. 7 (5) (2016) 40-53.
• [24] C. Tunç, A. Sirma, Stability analysis of a class of generalized neutral equations, J. Comput. Anal. Appl. 12 (4) (2010) 754-759.
• [25] S. Xu, J. Lam, Improved delay-dependent stability criteria for time-delay systems, IEEE Trans. Automat. Control 50 (3) (2005) 384-387.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).