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Zbl 0902.93062
Sontag, Eduardo D.
Comments on integral variants of ISS. (English)
[J] Syst. Control Lett. 34, No.1-2, 93-100 (1998). ISSN 0167-6911

Summary: This note discusses two integral variants of the input-to-state stability (ISS) property, which represent nonlinear generalizations of $L^{2}$ stability, in much the same way that ISS generalizes $L^{\infty}$ 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 $K{\cal L}$ is proved as well.

MSC 2000:: *93D25 Input-output approaches to stability of control systems
93C10 Nonlinear control systems

Keywords: input-to-state stability; ISS; nonlinear stability; system gains; bilinear systems

Cited in: Zbl 1243.93004

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