Nonlinear Scaling of (i)ISS-Lyapunov Functions

Christopher M. Kellett, Fabian R. Wirth

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)

Abstract

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.

Original languageEnglish
Article number7163325
Pages (from-to)1087-1092
Number of pages6
JournalIEEE Transactions on Automatic Control
Volume61
Issue number4
DOIs
Publication statusPublished - 1 Apr 2016
Externally publishedYes

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