A small-gain theorem in the absence of strong IISS

Hiroshi Ito; Christopher M. Kellett

doi:10.1109/TAC.2018.2886955

A small-gain theorem in the absence of strong IISS

Hiroshi Ito^*, Christopher M. Kellett

^*Corresponding author for this work

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

6 Citations (Scopus)

Abstract

Previous small-gain results for interconnected integral input-to-state (iISS) systems have been restricted to systems that are strongly iISS. This paper removes this restriction by allowing cross terms between external inputs and states in the Lyapunov decrease of component systems, and subsequently constructing a nonseparable Lyapunov function. An example demonstrates the use of this new small-gain formulation.

Original language	English
Article number	8576598
Pages (from-to)	3897-3904
Number of pages	8
Journal	IEEE Transactions on Automatic Control
Volume	64
Issue number	9
DOIs	https://doi.org/10.1109/TAC.2018.2886955
Publication status	Published - Sept 2019
Externally published	Yes

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10.1109/TAC.2018.2886955

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title = "A small-gain theorem in the absence of strong IISS",

abstract = "Previous small-gain results for interconnected integral input-to-state (iISS) systems have been restricted to systems that are strongly iISS. This paper removes this restriction by allowing cross terms between external inputs and states in the Lyapunov decrease of component systems, and subsequently constructing a nonseparable Lyapunov function. An example demonstrates the use of this new small-gain formulation.",

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AU - Kellett, Christopher M.

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AB - Previous small-gain results for interconnected integral input-to-state (iISS) systems have been restricted to systems that are strongly iISS. This paper removes this restriction by allowing cross terms between external inputs and states in the Lyapunov decrease of component systems, and subsequently constructing a nonseparable Lyapunov function. An example demonstrates the use of this new small-gain formulation.

KW - Integral input-to-state stability (iISS)

KW - Interconnected systems

KW - Lyapunov methods

KW - Small-gain criteria

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JO - IEEE Transactions on Automatic Control

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A small-gain theorem in the absence of strong IISS

Abstract

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