Estimates for solutions of homogeneous time-delay systems: comparison of Lyapunov-Krasovskii and Lyapunov-Razumikhin techniques

In this contribution, the estimates for the response of time-delay systems with nonlinear homogeneous right-hand side of degree strictly greater than one are constructed. The existing results obtained via the Lyapunov--Razumikhin approach are reminded. Their proofs, revisited in the appendix, lead t...

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Bibliographic Details
Published inInternational journal of control Vol. 95; no. 11; pp. 3002 - 3011
Main Authors Portilla, Gerson, Alexandrova, Irina V., Mondié, Sabine, Zhabko, Alexey P.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 02.11.2022
Taylor & Francis Ltd
Subjects
Estimates
estimates for solutions
Homogeneous time-delay systems
Liapunov functions
Lyapunov-Krasovskii functionals
Nonlinear systems
Time delay systems
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Summary:In this contribution, the estimates for the response of time-delay systems with nonlinear homogeneous right-hand side of degree strictly greater than one are constructed. The existing results obtained via the Lyapunov--Razumikhin approach are reminded. Their proofs, revisited in the appendix, lead to explicit expressions of the involved constants. Based on a recently introduced Lyapunov-Krasovskii functional and known estimates of the domain of attraction, we present new estimates of the system response. Using the same Lyapunov function in the Lyapunov-Razumikhin approach and in construction of the Lyapunov-Krasovskii functional, we compare both approaches and discuss the illustrative examples.
ISSN:0020-7179
1366-5820
DOI:10.1080/00207179.2021.1949045