Using an estimate for the matrizant of a linear system without pulse action, we obtain an exponential estimate for the matrizant of the corresponding system with pulse action at fixed times. The behavior of the partial derivatives of this matrizant with respect to a small parameter ε is examined.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. M. Samoilenko and N. A. Perestyuk, Impulsive Differential Equations [in Russian], Vyshcha Shkola, Kiev (1987).
N. A. Perestyuk, V. A. Plotnikov, A. M. Samoilenko, and N. V. Skripnik, Impulsive Differential Equations with Multivalued and Discontinuous Right-Hand Sides [in Russian], Institute of Mathematics, Ukrainian National Academy of Sciences, Kiev (2007).
R. I. Petryshyn and T. M. Sopronyuk, “Averaging of initial-value and boundary-value problems for one class of oscillatory impulsive systems,” Nelin. Kolyvannya, 9, No. 1, 68–84 (2006); English translation: Nonlin. Oscillations, 9, No. 1, 65–82 (2006).
Author information
Authors and Affiliations
Additional information
Translated from Neliniini Kolyvannya, Vol. 14, No. 1, pp. 85–92, January–March, 2011.
Rights and permissions
About this article
Cite this article
Petryshyn, R.I., Sopronyuk, T.M. Properties of the matrizant of a linear system with pulse action at fixed times. Nonlinear Oscill 14, 86–94 (2011). https://doi.org/10.1007/s11072-011-0143-3
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11072-011-0143-3