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Article

Further Results on the Input-to-State Stability of a Linear Disturbed System with Control Delay

by
Daniela Enciu
,
Adrian Toader
and
Ioan Ursu
*
National Institute for Aerospace Research “Elie Carafoli”—INCAS Bucharest, 061126 Bucharest, Romania
*
Author to whom correspondence should be addressed.
Mathematics 2024, 12(5), 634; https://doi.org/10.3390/math12050634
Submission received: 12 January 2024 / Revised: 7 February 2024 / Accepted: 18 February 2024 / Published: 21 February 2024
(This article belongs to the Special Issue The Delay Differential Equations and Their Applications)
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Abstract

In this paper, a theorem is obtained that gives sufficient input-to-state stability conditions for linear systems with control delay and additive disturbances. Stabilizing feedback is considered available in the absence of delay and disturbances. The mathematical tools are the Lyapunov–Krasovskii functional, the Jensen inequality and the double Hadamard inequality. The critical delay is highlighted.
Keywords: control delay; input-to-state-stability; Lyapunov–Krasovskii functionals; linear disturbed systems; critical delay control delay; input-to-state-stability; Lyapunov–Krasovskii functionals; linear disturbed systems; critical delay

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MDPI and ACS Style

Enciu, D.; Toader, A.; Ursu, I. Further Results on the Input-to-State Stability of a Linear Disturbed System with Control Delay. Mathematics 2024, 12, 634. https://doi.org/10.3390/math12050634

AMA Style

Enciu D, Toader A, Ursu I. Further Results on the Input-to-State Stability of a Linear Disturbed System with Control Delay. Mathematics. 2024; 12(5):634. https://doi.org/10.3390/math12050634

Chicago/Turabian Style

Enciu, Daniela, Adrian Toader, and Ioan Ursu. 2024. "Further Results on the Input-to-State Stability of a Linear Disturbed System with Control Delay" Mathematics 12, no. 5: 634. https://doi.org/10.3390/math12050634

APA Style

Enciu, D., Toader, A., & Ursu, I. (2024). Further Results on the Input-to-State Stability of a Linear Disturbed System with Control Delay. Mathematics, 12(5), 634. https://doi.org/10.3390/math12050634

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