On Exponential Stability of Volterra Difference Equations with Infinite Delay

• Autorzy: Ngoc P. H. A. , Hieu L. T.

Identyfikatory

DOI

10.4064/ba62-2-3

• Języki publikacji: EN

Abstrakty

EN

General nonlinear Volterra difference equations with infinite delay are considered. A new explicit criterion for global exponential stability is given. Furthermore, we present a stability bound for equations subject to nonlinear perturbations. Two examples are given to illustrate the results obtained.

Słowa kluczowe

EN

global exponential stability; infinite delay; phase space; Volterra difference equation

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2014
• Tom: Vol. 62, no 2
• Strony: 125--137
• Opis fizyczny: Bibliogr. 25 poz.

Twórcy

autor

Ngoc P. H. A.

• Department of Mathematics Vietnam National University-HCMC International University, Saigon, Vietnam

autor

Hieu L. T.

• Department of Mathematics Dong Thap University Dong Thap province, Vietnam

Bibliografia

• [ACF] R. P. Agarwal, C. Cuevas and M. V. S. Frasson, Semilinear functional difference equations with infinite delay, Math. Computer Modelling 55 (2012),
• 1083-1105.
• [BK12] E. Braverman and I. Karabash, Bohl-Perron-type stability theorems for linear difference equations with infinite delay, J. Difference Equations Appl. 18
• (2012), 909-939.
• [BK13] E. Braverman and I. Karabash, Structured stability radii and exponential stability tests for Volterra difference systems, Comput. Math. Appl. 66 (2013),
• 2259-2280.
• [BH] H. Brunner and P. J. Houwen, The Numerical Solution of Volterra Equations, CWI Monographs, North-Holland, Amsterdam, 1986.
• [CKRV98] M. R. Crisci, V. B. Kolmanovskii, E. Russo and A. Vecchio, Stability of difference Volterra equations: direct Liapunov method and numerical procedure, Comput. Math. Appl. 36 (1998), 77-97.
• [CKRV00] M. R. Crisci, V. B. Kolmanovskii, E. Russo and A. Vecchio, On the exponential stability of discrete Volterra equations, J. Difference Equations Appl. 6 (2000), 667-680.
• [CDCS] C. Cuevas, F. Dantas, M. Choquehuanca and H. Soto, lp-boundedness properties for Volterra difference equations, Appl. Math. Comput. 219 (2013),
• 6986-6999.
• [E05] S. Elaydi, An Introduction to Difference Equations, Springer, 2005.
• [E09] S. Elaydi, Stability and asymptoticity of Volterra difference equations: A progress report, J. Comput. Appl. Math. 228 (2009), 504-513.
• [ES] S. Elaydi and S. Murakami, Asymptotic stability versus exponential stability in linear Volterra difference equations of convolution type, J. Difference Equations Appl. 2 (1996), 401-410.
• [HS] D. Hinrichsen and N. K. Son, Stability radii of positive discrete-time equations underäne parameter perturbations, Int. J. Robust Nonlinear Control 8 (1998), 1169-1188.
• [KCT] V. B. Kolmanovskii, E. Castellanos-Velasco and J. A. Torres-Munoz, A survey: stability and boundedness of Volterra difference equations, Nonlinear Anal. 53 (2003), 861-928.
• [L] N. Levinson, A nonlinear Volterra equation arising in the theory of superuidity, J. Math. Anal. Appl. 1 (1960), 1-11.
• [MW] W. R. Mann and F. Wolf, Heat transfer between solids and gases under nonlinear boundary conditions, Quart. Appl. Math. 9 (1951), 163-184.
• [MM] H. Matsunaga and S. Murakami, Asymptotic behavior of solutions of functional difference equations, J. Math. Anal. Appl. 305 (2005), 391-410.
• [M97] S. Murakami, Representation of solutions of linear functional difference equations in phase space, Nonlinear Anal. 30 (1997), 1153-1164.
• [NH] P. H. A. Ngoc and L. T. Hieu, New criteria for exponential stability of nonlinear difference systems with time-varying delay, Int. J. Control 86 (2013), 1646-1651.
• [NNSM] P. H. A. Ngoc, T. Naito, J. S. Shin and S. Murakami, Stability and robust stability of positive linear Volterra difference equations, Int. J. Robust Nonlinear Control 19 (2008), 552-568.
• [PP] C. G. Philos and I. K. Purnaras, The behavior of solutions of linear Volterra difference equations with infinite delay, Comput. Math. Appl. 47 (2004), 1555-1563.
• [RD] Y. N. Raffoul and Y. M. Dib, Boundedness and stability in nonlinear discrete systems with nonlinear perturbation, J. Difference Equations Appl. 9 (2003), 853-862.
• [SB] Y. Song and C. T. H. Baker, Perturbation of Volterra difference equations, J. Difference Equations Appl. 10 (2004), 379-397.