Lyapunov-Razumikhin Methods for Stabilization in the Sample-and-Hold Sense of Retarded Nonlinear Systems

Abstract

A new methodology for the design of stabilizers in the sample-and-hold sense for nonlinear retarded systems is provided. It is shown that, if there exist a control LyapunovRazumikhin function and an induced steepest descent state feedback, uniformly in time bounded on bounded subsets of the state space, then such feedback, applied by suitably fast sampling and holding, guarantees practical semiglobal stability, with arbitrary small final target ball of the origin.