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Lyapunov-Krasovskii characterizations of integral input-to-state stability of delay systems with non-strict dissipation rates

Abstract : We provide several characterizations of integral input-to-state stability (iISS) of time-delay systems. These characterizations differ in the way the considered Lyapunov-Krasovskii functionals (LKF) dissipate along the solutions of the system. This dissipation can involve the LKF itself, as in existing iISS characterizations, but can alternatively involve the instantaneous value of the solution's norm (point-wise dissipation), the supremum norm of the state history (history-wise dissipation) or a mix of the two ( KL dissipation). We show that all of them guarantee iISS. By relying on a recent converse result by Y. Lin \& Y. Wang, we show that most of them are also necessary for iISS. These relaxed dissipation rates simplify the iISS analysis of time-delay systems and contribute to uniforming iISS theory with that of input-free systems. Proofs rely on several results for time-delay systems that may be of interest on their own, including a novel characterization of global asymptotic stability and the fact that iISS is equivalent to global asymptotic stability of the input-free system plus a uniform bounded energy-bounded state property.
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https://hal-centralesupelec.archives-ouvertes.fr/hal-03520499
Contributor : Antoine Chaillet Connect in order to contact the contributor
Submitted on : Tuesday, January 11, 2022 - 9:42:06 AM
Last modification on : Tuesday, May 17, 2022 - 12:04:09 PM

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Antoine Chaillet, Gokhan Goksu, Pierdomenico Pepe. Lyapunov-Krasovskii characterizations of integral input-to-state stability of delay systems with non-strict dissipation rates. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2021, pp.1-14. ⟨10.1109/TAC.2021.3099453⟩. ⟨hal-03520499⟩

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