Abstract
A piecewise constant control that solves the boundary value problem for linear impulsive differential systems is considered. We establish a necessary and sufficient conditions for the existence of such control. Moreover, a result that explicitly characterizes the solving control is presented.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bainov D.D., Simeonov P.S.: Systems with Impulse Effect: Stability, Theory and Applications. Wiley, New York (1989)
Samoilenko A.M., Perestyuk N.A.: Impulsive differential equations. World Scientific Publishing Co., Singapore New Jersey London Hong Kong (1995)
Hu S., Lakshmikantham V., Leela S.: Impulsive Differential Systems and the Pulse Phenomena. J. Math. Anal. App., 137, 605–612 (1989)
Nieto J.J.: Periodic Boundary Value Problems for First Order Impulsive Ordinary Differential Equations. Nonlinear Anal., 51, 1223–1232 (2002)
Bainov D., Hristova S., Hu S., Lakshmikantham V.: Periodic Boundary Value Problems for Systems of First order Impulsive Differential Equations. Differential Integral Equations, 2, 37–43 (1989)
Bainov D.D., Simeonov P.S.: Impulsive Differential Equations, Asymptotic Properties of the solution. World Scientific Publishers, Singapore (1995)
Akhmet M.U.: On the General Problrm of Stability for Impulsive Differential Equations. J. Math. Anal. Appl. 288(1), 182–196 (2003)
Leela, S., Marae F.A., Sivasundaram S.: Controllability of Impulsive Differential Equations. J. Math. Anal. Appl., 177(1), 24–30 (1993)
Benzaid Z., Sznaier M.: Constrained Controllability of Linear Impulse Differential System. IEEE Trans. Automat. Contr., 39, 1064–1066 (1994)
Akhmetov M.U., Perestyuk N.A., Tleubergenova M.A.: Control over linear pulse systems, Ukrain. Math. Zh., 47(3), 307–314 (1995)
Akhmetov M.U., Sejilova R.: The Control of the Boundary Value problem for linear impulsive integro-differential systems. J. Math. Anal. Appl., 236, 312–326 (1999)
Guan, Z.H., Qian, T.H., Yu, X.: Controllability and Observability of Linear Time Varying Impulsive Systems. IEEE Trans. Circuits Syst. I., 49(8), 1198–1207 (2002)
Akhmetov, M.U., Zafer, A., Sejilova, R.D.: The Control of Boundary Value Problems for quasiinear impulsive integro-differential systems. Nonlinear Analysis, 48, 271–286 (2002)
Akhmet M.U., Zafer, A.: Controllability of Two-Point Nonlinear Boundary Value Problems by the Numerical-Analytical Method. Appl. Math. Comput., 151, 729–744 (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer
About this paper
Cite this paper
Alzabut, J.O. (2007). Piecewise constant control of boundary value problem for linear impulsive differential systems. In: Taş, K., Tenreiro Machado, J.A., Baleanu, D. (eds) Mathematical Methods in Engineering. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-5678-9_8
Download citation
DOI: https://doi.org/10.1007/978-1-4020-5678-9_8
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-5677-2
Online ISBN: 978-1-4020-5678-9
eBook Packages: EngineeringEngineering (R0)