Sampled-data global asymptotic stabilization of globally Lipschitz retarded switched systems

In this paper, we address the sampled-data global asymptotic stabilization of nonlinear globally Lipschitz retarded switched systems under arbitrary Lebesgue measurable switching signals. In particular, we show that if a mode-independent, globally Lipschitz state feedback is available and acts as a global stabilizer in continuous time, then applying this feedback via sampling and holding ensures global asymptotic stability, given a sufficiently fast sampling. Moreover, when the class of piecewise-continuous switching signal is considered, we prove that suitably fast sampling also guarantees global exponential stability. Finally, an example is provided to illustrate the obtained results.