Converse Lyapunov–Krasovskii theorem for ISS of neutral systems in Sobolev spaces

Denis Efimov; Emilia Fridman

doi:10.1016/j.automatica.2020.109042

Converse Lyapunov–Krasovskii theorem for ISS of neutral systems in Sobolev spaces

Denis Efimov^*, Emilia Fridman

^*Corresponding author for this work

School of Electrical Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

The conditions of existence of a Lyapunov–Krasovskii functional (LKF) for nonlinear input-to-state stable (ISS) neutral type systems are proposed. The system under consideration depends nonlinearly on the delayed state and the delayed state derivative, and satisfies the conditions for the existence and uniqueness of the solutions. The LKF and the system properties are defined in a Sobolev space of absolutely continuous functions with bounded derivatives.

Original language	English
Article number	109042
Journal	Automatica
Volume	118
DOIs	https://doi.org/10.1016/j.automatica.2020.109042
State	Published - Aug 2020

Keywords

Lyapunov–Krasovskii functional
Neutral time-delay systems
Stability

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10.1016/j.automatica.2020.109042

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abstract = "The conditions of existence of a Lyapunov–Krasovskii functional (LKF) for nonlinear input-to-state stable (ISS) neutral type systems are proposed. The system under consideration depends nonlinearly on the delayed state and the delayed state derivative, and satisfies the conditions for the existence and uniqueness of the solutions. The LKF and the system properties are defined in a Sobolev space of absolutely continuous functions with bounded derivatives.",

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author = "Denis Efimov and Emilia Fridman",

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AB - The conditions of existence of a Lyapunov–Krasovskii functional (LKF) for nonlinear input-to-state stable (ISS) neutral type systems are proposed. The system under consideration depends nonlinearly on the delayed state and the delayed state derivative, and satisfies the conditions for the existence and uniqueness of the solutions. The LKF and the system properties are defined in a Sobolev space of absolutely continuous functions with bounded derivatives.

KW - Lyapunov–Krasovskii functional

KW - Neutral time-delay systems

KW - Stability

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Converse Lyapunov–Krasovskii theorem for ISS of neutral systems in Sobolev spaces

Abstract

Keywords

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