- Title
- Nonlinear scaling of (i)ISS-Lyapunov functions
- Creator
- Kellett, Christopher M.; Wirth, Fabian R.
- Relation
- ARC.FT1101000746
- Relation
- IEEE Transactions on Automatic Control Vol. 61, Issue 4, p. 1087-1092
- Publisher Link
- http://dx.doi.org/10.1109/TAC.2015.2458471
- Publisher
- Institute of Electrical and Electronics Engineers (IEEE)
- Resource Type
- journal article
- Date
- 2016
- Description
- While nonlinear scalings of Lyapunov functions are also Lyapunov functions, we provide examples that the same statement does not necessarily hold for Input-to-State Stable (ISS) Lyapunov functions or for integral ISS (iISS) Lyapunov functions. We provide sufficient conditions under which a nonlinear scaling of an ISS or iISS Lyapunov function is also an ISS or iISS Lyapunov function. We also introduce a generalization of the iISS Lyapunov function, which we term a dissipative iISS-Lyapunov function, that allows for a larger class of nonlinear scalings so that nonlinear scalings of dissipative iISS-Lyapunov functions are again dissipative iISS-Lyapunov functions.
- Subject
- nonlinear scalings; input-to-state stability (ISS); Lyapunov methods
- Identifier
- http://hdl.handle.net/1959.13/1325240
- Identifier
- uon:25222
- Identifier
- ISSN:0018-9286
- Rights
- © 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works
- Language
- eng
- Full Text
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