Abstract
This chapter is devoted to study the exponential stability of impulsive time-delay systems on time scales. Section 9.1 introduces and formulates impulsive time-delay systems on time scales. In Section 9.2, global exponential stability is discussed and sufficient conditions are provided by using Lyapunov-Razumikhin technique. Exponential stability is studied in Section 9.3 by the method of Lyapunov functionals. Stability results presented in this chapter extend and generalize the results introduced in Chapter 2 for discrete-time impulsive systems with time-delay to impulsive time-delay systems on hybrid time domains.
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
References
Y. Ma, J. Sun, Stability criteria of delayed impulsive systems on time scales. Nonlinear Anal. Theory Methods Appl. 67(4), 1181–1189 (2007)
Y. Ma, J. Sun, Stability in terms of two measures of impulsive time-delay systems on time scales. Acta Math. Sinica Chin. Ser. 51(4), 755–760 (2008)
J.G. Mesquita, Measure functional differential equations and impulsive functional dynamic equations on time scales. PhD Thesis, Universidade de Sao Paulo, Sao Carlos (2012)
Q. Wang, X. Liu, Exponential stability for impulsive delay differential equations by Razumikhin method. J. Math. Anal. Appl. 309(2), 462–473 (2005)
Q. Wang, X. Liu, Impulsive stabilization of delay differential systems via the Lyapunov – Razumikhin method. Appl. Math. Lett. 20(8), 839–845 (2007)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Liu, X., Zhang, K. (2019). Exponential Stability of Impulsive Time-Delay Systems on Time Scales. In: Impulsive Systems on Hybrid Time Domains. IFSR International Series in Systems Science and Systems Engineering, vol 33. Springer, Cham. https://doi.org/10.1007/978-3-030-06212-5_9
Download citation
DOI: https://doi.org/10.1007/978-3-030-06212-5_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-06211-8
Online ISBN: 978-3-030-06212-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)