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

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
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### References:

 [4] Isidori, A., Global almost disturbance decoupling with stability for non minimum-phase single-input single-output nonlinear systems, Systems Control Lett., 28, 115-122 (1996) · Zbl 0877.93055 [6] Praly, L.; Wang, Y., Stabilization in spite of matched unmodelled dynamics and an equivalent definition of input-to-state stability, Math. Control Signals Systems, 9, 1-33 (1996) · Zbl 0869.93040 [9] Sontag, E. D.; Wang, Y., On characterizations of the input-to-state stability property, Systems Control Lett., 24, 351-359 (1995) · Zbl 0877.93121 [10] Sontag, E. D.; Wang, Y., New characterizations of the input to state stability property, IEEE Trans. Automat. Control, 41, 1283-1294 (1996) · Zbl 0862.93051
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