214
Views
10
CrossRef citations to date
0
Altmetric
Articles

Stability of coupled functional differential-difference equations

Pages 1920-1930 | Received 18 Jan 2018, Accepted 13 Oct 2018, Published online: 03 May 2019

References

  • Berman, A., & Plemmons, R. J. (1979). Nonnegative matrices in mathematical sciences. New York, NY: Academic Press.
  • Brayton, R. K. (1967). Nonlinear oscillations in a distributed network. Quarterly of Applied Mathematics, 24, 289–301. doi: 10.1090/qam/99914
  • Brayton, R. K. (1968). Small signal stability criterion for electrical networks containing lossless transmission lines. IBM Journal of Research and Development, 12, 431–440. doi: 10.1147/rd.126.0431
  • Dai, L. (1989). Singular control systems, (Lecture Notes in Control and Information Sciences), Vol. 118.
  • Dieudonné, j. (1988). Foundations of modern analysis. New York: Academic Press.
  • Gu, K. (2010). Stability problem of systems with multiple delay channels. Automatica, 46, 743–751. doi: 10.1016/j.automatica.2010.01.028
  • Gu, K., & Liu, Y. (2009). Lyapunov-Krasovskii functional for uniform stability of coupled differential-functional equations. Automatica, 45, 798–804. doi: 10.1016/j.automatica.2008.10.024
  • Halanay, A., & Rasvan, V. (1997). Stability radii for rome propagation models. IMA Journal of Mathematical Control and Information, 14, 95–107. doi: 10.1093/imamci/14.1.95
  • Hale, J. K., & Huang, W. (1995). Variation of constants for hybrid systems of functional differential equations. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 125, 1–12. doi: 10.1017/S0308210500030729
  • Hale, J. K., & Martinez Amores, P. (1977). Stability in neutral equations. Nonlinear Analysis: Theory, Methods & Applications, 1, 161–173. doi: 10.1016/0362-546X(77)90007-4
  • Kolmanovskii, V. B., & Myshkis, A. (1996). Applied theory of functional differential equations. The Netherlands: Kluwer: Dordrecht.
  • Li, H., & Gu, K. (2010). Discretized Lyapunov Krasovskii functional for coupled differential-difference equations with multiple delay channels. Automatica, 46, 902–909. doi: 10.1016/j.automatica.2010.02.007
  • Logemann, H., & Ryan, E. P. (2014). Ordinary differential equations: Analysis, qualitative theory and control. (Springer Undergraduate Mathematics Series), London: Springer-Verlag.
  • Martinez-Amores, P. (1979). Periodic solutions of coupled systems of differential and difference equations. Annali di Matematica Pura ed Applicata, 121, 171–186. doi: 10.1007/BF02412000
  • Mazenc, F., Ito, H., & Pepe, P. (2013). Construction of Lyapunov functionals for coupled differential and continuous time difference equations, Proceedings of the 52nd IEEE Conference on Decision and Control, pp. 2245–2250.
  • Ngoc, P. H. A. (2018). Exponential stability of coupled linear delay time-varying differential-difference equations. IEEE Transactions on Automatic Control, 63, 843–848. doi: 10.1109/TAC.2017.2732064
  • Ngoc, P. H. A., & Trinh, H. (2016). Novel criteria for exponential stability of linear neutral time-varying differential systems. IEEE Transactions on Automatic Control, 61, 1590–1594. doi: 10.1109/TAC.2015.2478125
  • Niculescu, S. I. (2001). Delay effects on stability: A robust control approach (In Lecture notes in control and information science, Vol. 269). London: Springer.
  • Pepe, P. (2005). On the asymptotic stability of coupled delay differential and continuous time difference equations. Automatica, 41, 107–112.
  • Pepe, P., Jiang, Z. P., & Fridman, E. (2008). A new Lyapunov-Krasovskii methodology for coupled delay differential and difference equations. International Journal of Control, 81, 107–115. doi: 10.1080/00207170701383780
  • Phat, V. N., & Sau, N. H. (2014). On exponential stability of linear singular positive delayed systems. Applied Mathematics Letters, 38, 67–72. doi: 10.1016/j.aml.2014.07.003
  • Rasvan, V. (1973). Absolute stability of a class of control processes described by functional differential equations of neutral type. In: P. Janssens, J. Mawhin, and N. Rouche (Eds), Equations differentielles et fonctionelles nonlineaires. Paris: Hermann.
  • Rasvan, V. (2006). Functional differential equations of lossless propagation and almost linear behavior. IFAC Proceedings, 39, 138–150. doi: 10.3182/20060710-3-IT-4901.00024
  • Rasvan, V., & Niculescu, S. I. (2002). Oscillations in lossless propagation models: A Lyapunov-Krasovskii approach. IMA Journal of Mathematical Control and Information, 19, 157–172. doi: 10.1093/imamci/19.1_and_2.157
  • Shen, J., & Zheng, W. X. (2015). Positivity and stability of coupled differential-difference equations with time-varying delays. Automatica, 57, 123–127. doi: 10.1016/j.automatica.2015.04.007
  • Slemrod, M. (1971). Nonexistence of oscillations in a nonlinear distributed network. Journal of Mathematical Analysis and Applications, 36, 22–40. doi: 10.1016/0022-247X(71)90016-3
  • Sontag, E. D. (2013). Mathematical control theory: Deterministic finite dimensional systems. Heidelberg: Springer-Verlag Berlin.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.