Relationships between Subclasses of Integral Input-to-State Stability

Christopher M. Kellett; Peter M. Dower; Hiroshi Ito

doi:10.1109/TAC.2016.2598165

Relationships between Subclasses of Integral Input-to-State Stability

Christopher M. Kellett, Peter M. Dower, Hiroshi Ito

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

A certain "qualitative equivalence" has been recently demonstrated between integral input-to-state stability (iISS) and a nonlinear L₂-gain property. Furthermore, it has been observed that the properties of strong iISS and nonlinear L₂-gain are preserved when multiple systems satisfying the respective property are connected in cascade. This technical note clarifies the relationships between various input-to-state stability and (non)linear L_p-gain properties.

Original language	English
Article number	7533458
Pages (from-to)	2476-2482
Number of pages	7
Journal	IEEE Transactions on Automatic Control
Volume	62
Issue number	5
DOIs	https://doi.org/10.1109/TAC.2016.2598165
Publication status	Published - May 2017
Externally published	Yes

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10.1109/TAC.2016.2598165

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title = "Relationships between Subclasses of Integral Input-to-State Stability",

abstract = "A certain {"}qualitative equivalence{"} has been recently demonstrated between integral input-to-state stability (iISS) and a nonlinear L2-gain property. Furthermore, it has been observed that the properties of strong iISS and nonlinear L2-gain are preserved when multiple systems satisfying the respective property are connected in cascade. This technical note clarifies the relationships between various input-to-state stability and (non)linear Lp-gain properties.",

keywords = "Integral input-to-state stability, Lyapunov methods, nonlinear L-gain",

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AU - Dower, Peter M.

AU - Ito, Hiroshi

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N2 - A certain "qualitative equivalence" has been recently demonstrated between integral input-to-state stability (iISS) and a nonlinear L2-gain property. Furthermore, it has been observed that the properties of strong iISS and nonlinear L2-gain are preserved when multiple systems satisfying the respective property are connected in cascade. This technical note clarifies the relationships between various input-to-state stability and (non)linear Lp-gain properties.

AB - A certain "qualitative equivalence" has been recently demonstrated between integral input-to-state stability (iISS) and a nonlinear L2-gain property. Furthermore, it has been observed that the properties of strong iISS and nonlinear L2-gain are preserved when multiple systems satisfying the respective property are connected in cascade. This technical note clarifies the relationships between various input-to-state stability and (non)linear Lp-gain properties.

KW - Integral input-to-state stability

KW - Lyapunov methods

KW - nonlinear L-gain

UR - https://www.scopus.com/pages/publications/85018957221

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DO - 10.1109/TAC.2016.2598165

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ER -

Relationships between Subclasses of Integral Input-to-State Stability

Abstract

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