CONNECTIONS BETWEEN RAZUMIKHIN-TYPE THEOREMS AND THE ISS NONLINEAR SMALL GAIN THEOREM

A Razumikhin-type theorem that guarantees input-to-state Stability for functional differential equations viith disturbances is established u sing the nonlinear small-gain theorem. The result is used to show that input-to-state stabilizability for nonlinear finite-dimensional contr ol systems is robust, in an appropriate sense, to small time delays at the input. Also, relaxed Razumikhin-type conditions guaranteeing glob al asymptotic stability for differential difference equations are give n.