Affiliation:
1. Obafemi Awolowo University
2. University of Ibadan
Abstract
In this paper, the problem of asymptotic stability of a kind of nonlinear perturbed neutral differential system with variable delay is discussed. The Lyapunov-Krasovskii functional constructed, is used to obtain conditions for asymptotic stability of the nonlinear perturbed neutral differential system in terms of linear matrix inequality (LMI). The two new results (delay-independent and delay-dependent criteria) include and extend the existing results in the literature. Finally, an example of delay-dependent criteria is supplied and the simulation result is shown to justify the effectiveness and reliability of the used techniques.
Publisher
Mathematical Sciences and Applications E-Notes
Reference29 articles.
1. [1] Ademola, A. T., Arawomo, P. O.: Uniform stability and boundedness of solutions of nonlinear delay differential equations of the third order. Mathematical Journal of Okayama University. 55, 157-166 (2013).
2. [2] Ademola, A. T., Arawomo, P. O., Ogunlaran, O. M., Oyekan, E. A.: Uniform stability, boundedness and asymptotic behaviour of solutions of some third order nonlinear delay differential equations. Differential Equations and Control Processes, (4), 43-66 (2013).
3. [3] Ademola, A. T., Moyo, S., Ogundiran, M. O. Arawomo, P. O., Adesina, O. A.: Stability and boundedness of solution to a certain second-order non-autonomous stochastic differential equation. International Journal of Analysis. (2016) http://dx.doi.org/10.1155/2016/2012315.
4. [4] Ademola, A. T., Ogundare, B. S., Ogundiran, M. O., Adesina, O. A.: Periodicity, stability and boundedness of
solutions to certain second-order delay differential equations. International Journal of Differential equations. Article ID 2843709, 10 pages (2016).
5. [5] Ademola, A. T.: Asymptotic behaviour of solutions to certain nonlinear third order neutral functional differential equation. Heliyon 7, 1-8 (2021).