Complete type functional approach to input to state stability of time-delay systems

This note addresses the study of input to state stability of nonlinear time-delay systems that are linearizable in the first approximation. It is established that, under mild conditions, the so-called complete type functional of the associated linear systems with delay is a Local Input to State Lyap...

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Bibliographic Details
Published in:Systems & control letters 2024-04, Vol.186, p.105761, Article 105761
Main Authors: Gomez, Marco A., Mondié, Sabine
Format: Article
Language:English
Subjects:
Complete type functional
Delay Lyapunov matrix
Input to state stability
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Summary:This note addresses the study of input to state stability of nonlinear time-delay systems that are linearizable in the first approximation. It is established that, under mild conditions, the so-called complete type functional of the associated linear systems with delay is a Local Input to State Lyapunov–Krasovskii functional. Moreover, this complete type functional, which is fully defined by the delay Lyapunov matrix whenever the linear system is stable, allows the effective computation of the gains characterizing the input to state stability properties. An example illustrates the presented results. •Complete type functionals are used to study ISS of a class of time-delay systems.•A constructive approach for studying Local Input to State Stable systems is provided.•The approach allows the computation of the ISS gains.
ISSN:0167-6911
1872-7956
DOI:10.1016/j.sysconle.2024.105761