This talk deals with a structural aspect of control systems - their behavior under parameter variation with respect to local and global properies. Global properties include aspects of controllability and (practical) feedback stabilization, which may change as a parameter varies within a given set. We present persistence and continuity results for control and stabilization, which also give new insight into (uncontrolled) dynamical systems when applied to systems with small control range. The mathematical techniques are based on the study of transitivity of associated control flows. Local properties include aspects of robust stability and feedback stabilization. A control theoretic version of multiplicative ergodic theory shows that the spectrum of a control system consists of intervals. As the endpoints of these intervals pass through zero, the system changes its stability and stabilization behavior. Again, for small control range these results specialize to local bifurcation theory of dynamical systems.