Quantitative aspects of the input-to-state stability property

L. Grüne: Quantitative aspects of the input-to-state stability property
in: Proceedings of the Mathematical Theory of Networks and Systems (MTNS2002), CD-Rom, Article TUA4-4, South Bend, Indiana, 2002,

Smart-Link: http://www.nd.edu/~mtns/
Keywords: input-to-state stability; input-to-state dynamic stability; nonlinear stability theory; Lyapunov functions
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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.

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