- 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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