Quantitative aspects of the input-to-state stability property

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Grüne, Lars:
Quantitative aspects of the input-to-state stability property.
Bayreuth , 2002

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Abstract

In this paper we consider quantitative aspects of the input--to--state stability (ISS) property. Our considerations lead to a new variant of ISS, called input--to--state dynamical stability (ISDS), which is based on using a one--dimensional dynamical system for building the class KL function for the decay estimate and for describing the influence of the perturbation. The main feature of ISDS is that it admits a quantitative or gain preserving Lyapunov function characterization. We also show the relation to the original ISS formulation and present several applications.