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New Exponential Stability Criteria for Certain Neutral Integro-Differential Equations

Yıl 2020, Cilt: 13 Sayı: ÖZEL SAYI I, 119 - 131, 28.02.2020
https://doi.org/10.18185/erzifbed.638208

Öz



Bu çalışmada, birinci basamaktan
ayrık ve değişken gecikmeli neutral integro- diferansiyel denklemlerin (NIDE)
sıfır çözümünün üstel kararlılığı incelenmektedir. Uygun bir Lyapunov-Krasovski
fonksiyeli, Leibniz-Newton formülü ve matris eşitsizliği yardımıyla ele alınan
denklemin sıfır çözümünün üstel kararlılığı için yeter şartlar içeren yeni bir
sonuç ispatlanmaktadır. Bu çalışma literatürdeki konuyla ilgili önceki
sonuçları genişletmekte ve geliştirmektedir.



Kaynakça

  • ReferencesAgarwal, R. P.; Grace, S. R. 2000. ‘Asymptotic stability of certain neutral diffferential equations’. Math. Comput. Modelling 31, no. 8-9, 9–15.
  • Boyd, Stephen; El Ghaoui, Laurent; Feron, Eric; Balakrishnan, Venkataramanan, 1994. ‘Linear matrix inequalities in system and control theory’. SIAM Studies in Applied Mathematics, 15. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA,
  • Chen, Huabin; Meng, Xuejing, 2011. ‘An improved exponential stability criterion for a class of neutral delayed differential equations’. Appl. Math. Lett. 24, no. 11, 1763–1767.
  • Chen, Huabin, 2012. ‘Some improved criteria on exponential stability of neutral differential equation’. Adv. Difference Equ., 2012:170, 9 pp.
  • Chatbupapan, Watcharin; Mukdasai, Kanit, 2016. ‘New delay-range-dependent exponential stability criteria for certain neutral differential equations with interval discrete and distributed time- varying delays’. Adv. Difference Equ., Paper No. 324, 18 pp.
  • Deng, Shaojiang; Liao, Xiaofeng; Guo, Songtao, 2009. ‘Asymptotic stability analysis of certain neutral differential equations: a descriptor system approach’. Math. Comput. Simulation 79, no. 10, 2981–2993.
  • El-Morshedy, H. A.; Gopalsamy, K., 2000. ‘Nonoscillation, oscillation and convergence of a class of neutral equations’. Lakshmikantham's legacy: a tribute on his 75th birthday. Nonlinear Anal. 40, no. 1-8, Ser. A: Theory Methods, 173–183.
  • Fridman, E. 2001. ‘New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems’. Systems Control Lett. 43, no. 4, 309–319.
  • Fridman, Emilia, 2002. ‘Stability of linear descriptor systems with delay: a Lyapunov-based approach’. J. Math. Anal. Appl. 273, no. 1, 24–44.
  • Gu, Keqin; Kharitonov, Vladimir L.; Chen, Jie, 2003. ‘Stability of time-delay systems’. Control Engineering. Birkhäuser Boston, Inc., Boston, MA.
  • Gözen, Melek; Tunc, Cemil 2017. ‘On exponential stability of solutions of neutral differential systems with multiple variable delays’. Electron. J. Math. Anal. Appl. 5, no. 1, 17– 31.
  • Gözen, Melek; Tunç, Cemil 2017. ‘A note on the exponential stability of linear systems with variable retardations’. Appl. Math. Inf. Sci. 11, no. 3, 899–906.
  • Gözen, Melek; Tunç, Cemil 2018. ‘On the exponential stability of a neutral differential equation of first order’. J. Math. Appl. 41, 95–107.
  • Hale, Jack K.; Verduyn Lunel, Sjoerd M. 1993. ‘Introduction to functional-differential equations’. Applied Mathematical Sciences, 99. Springer- Verlag, New York.
  • Hristova, Snezhana; Tunc, Cemil 2019. ‘Stability of nonlinear Volterra integro-Differential equations with Caputo fractional derivative and bounded delays’. Electron. J. Differential Equations, Paper No. 30, 11 pp.
  • Kwon, O. M.; Park, Ju H., 2008. ‘On improved delay-dependent stability criterion of certain neutral differential equations’. Appl. Math. Comput. 199, no. 1, 385– 391.
  • Keadnarmol, Panuwat; Rojsiraphisal, Thaned, 2014. ‘Globally exponential stability of a certain neutral differential equation with time-varying delays’. Adv. Difference Equ., 32, 10 pp.
  • Liao, Xiaofeng; Liu, Yanbing; Guo, Songtao; Mai, Huanhuan, 2009. ‘Asymptotic stability of delayed neural networks: a descriptor system approach’. Commun. Nonlinear Sci. Numer. Simul. 14, no. 7, 3120–3133.
  • Li, Xiaodi 2009. ‘Global exponential stability for a class of neural networks’. Appl. Math. Lett. 22, no. 8, 1235–1239.
  • Li, Xiaodi; Fu, 2013. Xilin, ‘Effect of leakage time-varying delay on stability of nonlinear differential systems’. J. Franklin Inst. 350, no. 6, 1335–1344.
  • Nam, P. T.; Phat, V. N. 2009. ‘An improved stability criterion for a class of neutral differential equations’. Appl. Math. Lett. 22, no. 1, 31–35.
  • Park, J. H. 2004. ‘Delay-dependent criterion for asymptotic stability of a class of neutral equations’. Appl. Math. Lett. 17, no. 10, 1203– 1206.
  • Park, Ju H.; Kwon, O. M., 2008. ‘Stability analysis of certain nonlinear differential equation’. Chaos Solitons Fractals 37, no. 2, 450– 453.
  • Pinjai, Sirada; Mukdasai, Kanit, 2013. ‘New delay-dependent robust exponential stability criteria of LPD neutral systems with mixed time-varying delays and nonlinear perturbations’. J. Appl. Math., Art. ID 268905, 18 pp.
  • Rojsiraphisal, Thaned; Niamsup, Piyapong 2010. ‘Exponential stability of certain neutral differential equations’. Appl. Math. Comput. 217, no. 8, 3875–3880.
  • Sun, Yuan Gong; Wang, Long 2006. ‘Note on asymptotic stability of a class of neutral differential equations’. Appl. Math. Lett. 19, no. 9, 949–953.
  • Slyn’ko, Vitalii; Tunç, Cemil; 2019. ‘Stability of abstract linear switched impulsive differential equations’. Automatica J. IFAC 107, 433–441.
  • Tunç, Cemil; Altun, Melek 2012. ‘On the integrability of solutions of non-autonomous differential equations of second order with multiple variable deviating arguments’. J. Comput. Anal. Appl. 14, no. 5, 899–908.
  • Tunç, Cemil 2013. ‘Exponential stability to a neutral differential equation of first order with delay’. Ann. Differential Equations 29, no. 3, 253–256.
  • Tunç, Cemil; Mohammed, Sizar Abid 2017. ‘New results on exponential stability of nonlinear Volterra integro-differential equations with constant time-lag’. Proyecciones 36, no. 4,
  • Tunç, Cemil; Tunç, Osman 2018. ‘New results on the stability, integrability and boundedness in Volterra integro-differential equations’. Bull. Comput. Appl. Math. 6, no. 1, 41–58.

New Exponential Stability Criteria for Certain Neutral Integro-Differential Equations

Yıl 2020, Cilt: 13 Sayı: ÖZEL SAYI I, 119 - 131, 28.02.2020
https://doi.org/10.18185/erzifbed.638208

Öz

In this work, the exponential stability of zero solution of some neutral integro-differential equations of the first order (NIDE) with discrete and distributed time-varying delays is discussed. A new result that has sufficient conditions on the exponential stability of zero solution is proved by aid a new Lyapunov-Krasovskii functional, the Leibniz-Newton formula and a matrix inequality. The result of this paper extends and improves some former results on the topic in the literature.

Kaynakça

  • ReferencesAgarwal, R. P.; Grace, S. R. 2000. ‘Asymptotic stability of certain neutral diffferential equations’. Math. Comput. Modelling 31, no. 8-9, 9–15.
  • Boyd, Stephen; El Ghaoui, Laurent; Feron, Eric; Balakrishnan, Venkataramanan, 1994. ‘Linear matrix inequalities in system and control theory’. SIAM Studies in Applied Mathematics, 15. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA,
  • Chen, Huabin; Meng, Xuejing, 2011. ‘An improved exponential stability criterion for a class of neutral delayed differential equations’. Appl. Math. Lett. 24, no. 11, 1763–1767.
  • Chen, Huabin, 2012. ‘Some improved criteria on exponential stability of neutral differential equation’. Adv. Difference Equ., 2012:170, 9 pp.
  • Chatbupapan, Watcharin; Mukdasai, Kanit, 2016. ‘New delay-range-dependent exponential stability criteria for certain neutral differential equations with interval discrete and distributed time- varying delays’. Adv. Difference Equ., Paper No. 324, 18 pp.
  • Deng, Shaojiang; Liao, Xiaofeng; Guo, Songtao, 2009. ‘Asymptotic stability analysis of certain neutral differential equations: a descriptor system approach’. Math. Comput. Simulation 79, no. 10, 2981–2993.
  • El-Morshedy, H. A.; Gopalsamy, K., 2000. ‘Nonoscillation, oscillation and convergence of a class of neutral equations’. Lakshmikantham's legacy: a tribute on his 75th birthday. Nonlinear Anal. 40, no. 1-8, Ser. A: Theory Methods, 173–183.
  • Fridman, E. 2001. ‘New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems’. Systems Control Lett. 43, no. 4, 309–319.
  • Fridman, Emilia, 2002. ‘Stability of linear descriptor systems with delay: a Lyapunov-based approach’. J. Math. Anal. Appl. 273, no. 1, 24–44.
  • Gu, Keqin; Kharitonov, Vladimir L.; Chen, Jie, 2003. ‘Stability of time-delay systems’. Control Engineering. Birkhäuser Boston, Inc., Boston, MA.
  • Gözen, Melek; Tunc, Cemil 2017. ‘On exponential stability of solutions of neutral differential systems with multiple variable delays’. Electron. J. Math. Anal. Appl. 5, no. 1, 17– 31.
  • Gözen, Melek; Tunç, Cemil 2017. ‘A note on the exponential stability of linear systems with variable retardations’. Appl. Math. Inf. Sci. 11, no. 3, 899–906.
  • Gözen, Melek; Tunç, Cemil 2018. ‘On the exponential stability of a neutral differential equation of first order’. J. Math. Appl. 41, 95–107.
  • Hale, Jack K.; Verduyn Lunel, Sjoerd M. 1993. ‘Introduction to functional-differential equations’. Applied Mathematical Sciences, 99. Springer- Verlag, New York.
  • Hristova, Snezhana; Tunc, Cemil 2019. ‘Stability of nonlinear Volterra integro-Differential equations with Caputo fractional derivative and bounded delays’. Electron. J. Differential Equations, Paper No. 30, 11 pp.
  • Kwon, O. M.; Park, Ju H., 2008. ‘On improved delay-dependent stability criterion of certain neutral differential equations’. Appl. Math. Comput. 199, no. 1, 385– 391.
  • Keadnarmol, Panuwat; Rojsiraphisal, Thaned, 2014. ‘Globally exponential stability of a certain neutral differential equation with time-varying delays’. Adv. Difference Equ., 32, 10 pp.
  • Liao, Xiaofeng; Liu, Yanbing; Guo, Songtao; Mai, Huanhuan, 2009. ‘Asymptotic stability of delayed neural networks: a descriptor system approach’. Commun. Nonlinear Sci. Numer. Simul. 14, no. 7, 3120–3133.
  • Li, Xiaodi 2009. ‘Global exponential stability for a class of neural networks’. Appl. Math. Lett. 22, no. 8, 1235–1239.
  • Li, Xiaodi; Fu, 2013. Xilin, ‘Effect of leakage time-varying delay on stability of nonlinear differential systems’. J. Franklin Inst. 350, no. 6, 1335–1344.
  • Nam, P. T.; Phat, V. N. 2009. ‘An improved stability criterion for a class of neutral differential equations’. Appl. Math. Lett. 22, no. 1, 31–35.
  • Park, J. H. 2004. ‘Delay-dependent criterion for asymptotic stability of a class of neutral equations’. Appl. Math. Lett. 17, no. 10, 1203– 1206.
  • Park, Ju H.; Kwon, O. M., 2008. ‘Stability analysis of certain nonlinear differential equation’. Chaos Solitons Fractals 37, no. 2, 450– 453.
  • Pinjai, Sirada; Mukdasai, Kanit, 2013. ‘New delay-dependent robust exponential stability criteria of LPD neutral systems with mixed time-varying delays and nonlinear perturbations’. J. Appl. Math., Art. ID 268905, 18 pp.
  • Rojsiraphisal, Thaned; Niamsup, Piyapong 2010. ‘Exponential stability of certain neutral differential equations’. Appl. Math. Comput. 217, no. 8, 3875–3880.
  • Sun, Yuan Gong; Wang, Long 2006. ‘Note on asymptotic stability of a class of neutral differential equations’. Appl. Math. Lett. 19, no. 9, 949–953.
  • Slyn’ko, Vitalii; Tunç, Cemil; 2019. ‘Stability of abstract linear switched impulsive differential equations’. Automatica J. IFAC 107, 433–441.
  • Tunç, Cemil; Altun, Melek 2012. ‘On the integrability of solutions of non-autonomous differential equations of second order with multiple variable deviating arguments’. J. Comput. Anal. Appl. 14, no. 5, 899–908.
  • Tunç, Cemil 2013. ‘Exponential stability to a neutral differential equation of first order with delay’. Ann. Differential Equations 29, no. 3, 253–256.
  • Tunç, Cemil; Mohammed, Sizar Abid 2017. ‘New results on exponential stability of nonlinear Volterra integro-differential equations with constant time-lag’. Proyecciones 36, no. 4,
  • Tunç, Cemil; Tunç, Osman 2018. ‘New results on the stability, integrability and boundedness in Volterra integro-differential equations’. Bull. Comput. Appl. Math. 6, no. 1, 41–58.
Toplam 31 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Melek Gözen 0000-0002-7487-9869

Yayımlanma Tarihi 28 Şubat 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 13 Sayı: ÖZEL SAYI I

Kaynak Göster

APA Gözen, M. (2020). New Exponential Stability Criteria for Certain Neutral Integro-Differential Equations. Erzincan University Journal of Science and Technology, 13(ÖZEL SAYI I), 119-131. https://doi.org/10.18185/erzifbed.638208