Simultaneous stabilization of countable families of nonlinear systems by means of continuous feedback

In this paper, we show that given any countable family of general nonlinear systems, there exists a continuous feedback law that simultaneously stabilizes (not asymptotically) the family, if each system of the family is asymptotically stabilizable by means of continuous feedback. For any such family, we find two feedback laws that solve the simultaneous stabilization problem. The first one depends on a partition of unity while the second one is simpler and does not involve any partition of unity