Nonconservative Discrete-Time ISS Small-Gain Conditions for Closed Sets

Title: Nonconservative Discrete-Time ISS Small-Gain Conditions for Closed Sets
Creator: Noroozi, Navid; Geiselhart, Roman; Grüne, Lars; Rüffer, Björn S.; Wirth, Fabian R.
Relation: IEEE Transations on Automatic Control Vol. 63, Issue 5, p. 1231-1242
Publisher Link: http://dx.doi.org/10.1109/TAC.2017.2735194
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Resource Type: journal article
Date: 2018
Description: This paper presents a unification and a generalization of the small-gain theory subsuming a wide range of existing small-gain theorems. In particular, we introduce small-gain conditions that are necessary and sufficient to ensure input-to-state stability (ISS) with respect to closed sets. Toward this end, we first develop a Lyapunov characterization of ωISS via finite-step ωISS Lyapunov functions. Then, we provide the small-gain conditions to guarantee ωISS of a network of systems. Finally, applications of our results to partial ISS, ISS of time-varying systems, synchronization problems, incremental stability, and distributed observers are given.
Subject: input-to-state stability (ISS); large-scale discrete-time systems; Lyapunov methods; stability criteria
Identifier: http://hdl.handle.net/1959.13/1448087
Identifier: uon:43307
Identifier: ISSN:0018-9286
Language: eng
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