Comments on integral variants of ISS

Research output: Contribution to journalArticle

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Abstract

This note discusses two integral variants of the input-to-state stability (ISS) property, which represent nonlinear generalizations of L2 stability, in much the same way that ISS generalizes L stability. Both variants are equivalent to ISS for linear systems. For general nonlinear systems, it is shown that one of the new properties is strictly weaker than ISS, while the other one is equivalent to it. For bilinear systems, a complete characterization is provided of the weaker property. An interesting fact about functions of type script K signℒ is proved as well.

Original languageEnglish (US)
Pages (from-to)93-100
Number of pages8
JournalSystems and Control Letters
Volume34
Issue number1-2
DOIs
StatePublished - May 25 1998

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Linear systems
Nonlinear systems

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Computer Science(all)
  • Mechanical Engineering
  • Electrical and Electronic Engineering

Keywords

  • ISS
  • Input-to-state stability
  • Nonlinear stability
  • System gains

Cite this

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title = "Comments on integral variants of ISS",
abstract = "This note discusses two integral variants of the input-to-state stability (ISS) property, which represent nonlinear generalizations of L2 stability, in much the same way that ISS generalizes L∞ stability. Both variants are equivalent to ISS for linear systems. For general nonlinear systems, it is shown that one of the new properties is strictly weaker than ISS, while the other one is equivalent to it. For bilinear systems, a complete characterization is provided of the weaker property. An interesting fact about functions of type script K signℒ is proved as well.",
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author = "Eduardo Sontag",
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}

Comments on integral variants of ISS. / Sontag, Eduardo.

In: Systems and Control Letters, Vol. 34, No. 1-2, 25.05.1998, p. 93-100.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Comments on integral variants of ISS

AU - Sontag, Eduardo

PY - 1998/5/25

Y1 - 1998/5/25

N2 - This note discusses two integral variants of the input-to-state stability (ISS) property, which represent nonlinear generalizations of L2 stability, in much the same way that ISS generalizes L∞ stability. Both variants are equivalent to ISS for linear systems. For general nonlinear systems, it is shown that one of the new properties is strictly weaker than ISS, while the other one is equivalent to it. For bilinear systems, a complete characterization is provided of the weaker property. An interesting fact about functions of type script K signℒ is proved as well.

AB - This note discusses two integral variants of the input-to-state stability (ISS) property, which represent nonlinear generalizations of L2 stability, in much the same way that ISS generalizes L∞ stability. Both variants are equivalent to ISS for linear systems. For general nonlinear systems, it is shown that one of the new properties is strictly weaker than ISS, while the other one is equivalent to it. For bilinear systems, a complete characterization is provided of the weaker property. An interesting fact about functions of type script K signℒ is proved as well.

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KW - System gains

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