Formulas relating K L stability estimates of discrete-time and sampled-data nonlinear systems

We provide an explicit K L stability or input-to-state stability (ISS) estimate for a sampled-data nonlinear system in terms of the K L estimate for the corresponding discrete-time system and a K function describing inter-sample growth. Tt is quite obvious that a uniform inter-sample growth condition, plus an ISS properly for the exact discrete-time model of a closed-loop system, implies uniform TSS 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. (C) 1999 Elsevier Science B.V. All rights reserved.