Lyapunov-Krasovskii Characterizations of Integral Input-to-State Stability of Delay Systems With Nonstrict Dissipation Rates

Chaillet A., Goksu G., Pepe P.

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, cilt.67, sa.7, ss.3259-3272, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 67 Sayı: 7
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1109/tac.2021.3099453
  • Dergi Adı: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Business Source Elite, Business Source Premier, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.3259-3272
  • Anahtar Kelimeler: Lyapunov methods, FUNCTIONAL-DIFFERENTIAL EQUATIONS, ISS, IISS
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

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 (KL 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.