Comments on integral variants of ISS. (English) Zbl 0902.93062

Sontag, Eduardo D.

Syst. Control Lett. 34, No. 1-2, 93-100 (1998).

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 \(K{\mathcal L}\) is proved as well.

MSC:

93D25	Input-output approaches in control theory
93C10	Nonlinear systems in control theory

Keywords:

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

References:

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