- 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 lp-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 lp-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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