Vector L2-gain and stability of feedback switched systems

Jun Zhao; David J. Hill

doi:10.1016/j.automatica.2009.02.026

Vector L₂-gain and stability of feedback switched systems

Jun Zhao^*, David J. Hill

^*Corresponding author for this work

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

32 Citations (Scopus)

Abstract

A concept of vector L₂-gain is presented for switched systems. Each subsystem does not necessarily have L₂-gain in the classic sense but is assumed to have individual L₂-gain during any time interval when the subsystem is active. Stability is derived from this vector L₂-gain under some constraints on inactive storage functions. Asymptotic stability is also achieved if in addition a small-time norm-observability property is imposed. A small-gain theorem for feedback switched systems with vector L₂-gain assured for each subsystem is established. The small-gain condition is given in terms of the L₂-gains of the coupled active subsystems and the changes of inactive storage functions. A switching law design method is also given to achieve vector L₂-gain.

Original language	English
Pages (from-to)	1703-1707
Number of pages	5
Journal	Automatica
Volume	45
Issue number	7
DOIs	https://doi.org/10.1016/j.automatica.2009.02.026
Publication status	Published - Jul 2009

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title = "Vector L2-gain and stability of feedback switched systems",

abstract = "A concept of vector L2-gain is presented for switched systems. Each subsystem does not necessarily have L2-gain in the classic sense but is assumed to have individual L2-gain during any time interval when the subsystem is active. Stability is derived from this vector L2-gain under some constraints on inactive storage functions. Asymptotic stability is also achieved if in addition a small-time norm-observability property is imposed. A small-gain theorem for feedback switched systems with vector L2-gain assured for each subsystem is established. The small-gain condition is given in terms of the L2-gains of the coupled active subsystems and the changes of inactive storage functions. A switching law design method is also given to achieve vector L2-gain.",

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AU - Hill, David J.

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N2 - A concept of vector L2-gain is presented for switched systems. Each subsystem does not necessarily have L2-gain in the classic sense but is assumed to have individual L2-gain during any time interval when the subsystem is active. Stability is derived from this vector L2-gain under some constraints on inactive storage functions. Asymptotic stability is also achieved if in addition a small-time norm-observability property is imposed. A small-gain theorem for feedback switched systems with vector L2-gain assured for each subsystem is established. The small-gain condition is given in terms of the L2-gains of the coupled active subsystems and the changes of inactive storage functions. A switching law design method is also given to achieve vector L2-gain.

AB - A concept of vector L2-gain is presented for switched systems. Each subsystem does not necessarily have L2-gain in the classic sense but is assumed to have individual L2-gain during any time interval when the subsystem is active. Stability is derived from this vector L2-gain under some constraints on inactive storage functions. Asymptotic stability is also achieved if in addition a small-time norm-observability property is imposed. A small-gain theorem for feedback switched systems with vector L2-gain assured for each subsystem is established. The small-gain condition is given in terms of the L2-gains of the coupled active subsystems and the changes of inactive storage functions. A switching law design method is also given to achieve vector L2-gain.

KW - Feedback interconnection

KW - Stability

KW - Switched systems

KW - Vector L-gain

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DO - 10.1016/j.automatica.2009.02.026

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SP - 1703

EP - 1707

JO - Automatica

JF - Automatica

IS - 7

ER -

Vector L₂-gain and stability of feedback switched systems

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