Qualitative equivalences of ISS and l(p)-gain stability properties for discrete-time nonlinear systems

Title: Qualitative equivalences of ISS and l(p)-gain stability properties for discrete-time nonlinear systems
Creator: Tran, Duc N.; Kellett, Christopher M.; Dower, Peter M.
Relation: Automatica Vol. 77, Issue March, p. 360-369
Publisher Link: http://dx.doi.org/10.1016/j.automatica.2016.11.033
Publisher: Pergamon Press
Resource Type: journal article
Date: 2017
Description: Input-to-state stability (ISS) and input–output ℒ₂-gain are two important robust stability concepts in analyzing the interconnections of nonlinear dynamical systems. In this paper, we demonstrate several qualitative equivalences between different ISS related properties and l_p-gain properties for discrete-time systems via nonlinear changes of coordinates. Prior to that, certain summation-to-summation estimates are shown to be equivalent to the standard definitions of ISS and integral ISS (iISS) which lead to sufficient Lyapunov function conditions to verify l_p-gain properties. Combined with known results on the equivalence of 0-input global asymptotic stability and iISS, and a superposition principle, we subsequently outline interesting implicative relationships between various discrete-time robust stability properties.
Subject: input-to-state stability; discrete-time systems; nonlinear systems
Identifier: http://hdl.handle.net/1959.13/1398656
Identifier: uon:34470
Identifier: ISSN:0005-1098
Language: eng
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