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• W3211115055 abstract "In this article, 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 (LKFs) 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 (pointwise dissipation), the supremum norm of the state history (historywise dissipation), or a mix of the two ( <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>${mathcal K}{mathcal L}$</tex-math></inline-formula> dissipation). We show that all of them guarantee iISS. By relying on a recent converse result by Y. Lin and 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." @default.
• W3211115055 created "2021-11-08" @default.
• W3211115055 creator A5037636432 @default.
• W3211115055 creator A5051832041 @default.
• W3211115055 creator A5058680776 @default.
• W3211115055 date "2022-07-01" @default.
• W3211115055 modified "2023-10-04" @default.
• W3211115055 title "Lyapunov–Krasovskii Characterizations of Integral Input-to-State Stability of Delay Systems With Nonstrict Dissipation Rates" @default.
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• W3211115055 doi "https://doi.org/10.1109/tac.2021.3099453" @default.
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