| Formulas relating KL stability estimates of discrete-time and sampled-data nonlinear systems (2007) | |||||||||||||||
Abstract | |||||||||||||||
| We provide an explicit KL stability or input-to-state stability (ISS) estimate for a sampled-data nonlinear system in terms of the KL estimate for the corresponding discrete-time system and a K function describing inter-sample growth. It is quite obvious that a uniform inter-sample growth condition, plus an ISS property for the exact discrete-time model of a closed-loop system, implies uniform ISS of the sampled-data nonlinear system. Our results serve to quantify these facts by means of comparison functions. Our results can be used as an alternative to prove and extend results in [1] or extend some results in [4] to a class of nonlinear systems. Finally, the formulas we establish can be used as a tool for some other problems which we indicate. 1 Introduction There is a strong motivation for the investigation of sampled-data systems due to the prevalence of computer controlled systems (see [4, 5, 6]). Moreover, very often linear theory does not suffice and we need to deal with nonlin... | |||||||||||||||
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