  Selected results for the stability and optimal control of abstract switched
systems in Banach and Hilbert space are reviewed. The dynamics are typically
given in a piecewise sense by a family of nonlinearly perturbed evolutions of
strongly continuous semigroups. Stability refers to characterizations of
asymptotic decay of solutions that holds uniformly for certain classes of
switching signals for time going to infinity. Optimal control refers to the
minimization of costs associated to solutions by appropriately selecting
switching signals. Selected numerical results verify and visualize some of the
available theory.
