Convergence properties for discrete-time nonlinear systems

Title: Convergence properties for discrete-time nonlinear systems
Creator: Tran, Duc N.; Ruffer, Björn S.; Kellett, Christopher M.
Relation: IEEE Transactions on Automatic Control Vol. 64, Issue 8, p. 3415-3422
Publisher Link: http://dx.doi.org/10.1109/TAC.2018.2879951
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Resource Type: journal article
Date: 2019
Description: Three similar convergence notions are considered. Two of them are the long established notions of convergent dynamics and incremental stability. The other is the more recent notion of contraction analysis. All three convergence notions require that all solutions of a system converge to each other. In this paper, we investigate the differences between these convergence properties for discrete-time, time-varying nonlinear systems by comparing the properties in pairs and using examples. We also demonstrate a time-varying smooth Lyapunov function characterization for each of these convergence notions. In addition, with appropriate assumptions, we provide several sufficient conditions to establish relationships between these properties in terms of Lyapunov functions.
Subject: asymptotic stability; convergence; Lyapunov methods; nonlinear systems; stability criteria; time-varying systems
Identifier: http://hdl.handle.net/1959.13/1412341
Identifier: uon:36466
Identifier: ISSN:0018-9286
Language: eng
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