Summability criteria for stability of sets for sampled-data nonlinear inclusions

We present sufficient conditions for stability of parameterized difference inclusions that involve various summability criteria on functions of the trajectories of the system, to conclude global asymptotic stability and global exponential stability. Our theorems parallel similar results for continuous-time differential inclusions and extend previously published summability criteria for difference equations. They are tailored to be used within a framework for stabilization of sampled-data differential inclusions via their approximate discrete-time models, reported in a separate paper of this conference. We believe that these tools may become a useful addition to the "toolbox" for controller design for sampled-data nonlinear systems via their approximate discrete-time models