We consider a system of discrete equations containing variable delays and apply the averaging method to find the solution of this system. We propose new procedures for taking into account a given variable delay in the solution of the averaged system. It is shown that the solutions of the averaged and original systems are close.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
B. C. Kuo, Digital Control Systems, Oxford Univ. Press, New York (1995).
G. D’Antona and A. Ferrero, Digital Signal Processing for Measurement Systems: Theory and Applications, Springer, New York (2006).
E. L. Belan, “Averaging in the theory of finite-difference equations,” Ukr. Mat. Zh., 19, No. 3, 85–90 (1967); English translation : Ukr. Math. J., 19, No. 3, 319–323 (1967).
D. I. Martynyuk, V. I. Danilov, and V. G. Pan’kov, “Second Bogolyubov theorem for systems of difference equations,” Ukr. Mat. Zh., 48, No. 4, 464–475 (1996); English translation : Ukr. Math. J., 48, No. 4, 516–529 (1996).
V. A. Plotnikov, L. I. Plotnikova, and A. T. Yarovoi, “Averaging method for discrete systems and its application to control problems,” Nelin. Kolyv., 7, No. 2, 241–254 (2004); English translation : Nonlin. Oscillat., 7, No. 2, 240–253 (2004).
O. D. Kichmarenko and M. L. Karpycheva, “Averaging of the systems of discrete equations with constant delay,” Nauchn. Vestn. Uzhgorod. Univ., Ser. Mat. Informat., Issue 23, No. 2, 76–85 (2012).
O. D. Kichmarenko and M. L. Karpycheva, “Averaging of periodic controllable systems with constant delay on the discrete time,” Vestn. Odes. Univ., Ser. Mat. Mekh., 17, Issue 1–2, 54–69 (2012).
O. D. Kichmarenko and M. L. Karpycheva, “Averaging of discrete equations with periodic delay in control problems,” in: Proc. of the XIIth All-Russian Conference on Control Problems ACCP-2014 (electronic resource) [in Russian], Institute for the Problems of Control, Russian Academy of Sciences, Moscow (2014), pp. 1304–1316.
A. S. Apartsin, Nonclassical Volterra Problems of the First Kind: Theory and Numerical Methods [in Russian], Novosibirsk, Nauka (1999).
Author information
Authors and Affiliations
Additional information
Translated from Neliniini Kolyvannya, Vol. 19, No. 3, pp. 376–389, July–September, 2016.
Rights and permissions
About this article
Cite this article
Kichmarenko, O.D., Karpycheva, M.L. General Averaging Scheme for Discrete Equations with Variable Delay. J Math Sci 226, 270–284 (2017). https://doi.org/10.1007/s10958-017-3533-y
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-017-3533-y