The problem of simultaneously stabilizing a finite collection of non-linear systems is considered. A new and simple approach to designing a single state (linear) feedback control which simultaneously stabilizes this collection of non-linear systems is presented. The concepts of the function norm and the Bellman-Gronwall inequality are used to investigate the conditions for simultaneous stabilization. A design procedure for single state feedback control, is also presented. Several examples are given to demonstrate the validity of our results.