  This paper studies switching stabilization problems for continuous-time
switched linear systems. We consider four types of switching stabilizability
defined under different assumptions on the switching control input. The most
general switching stabilizability is defined as the existence of a measurable
switching signal under which the resulting time-varying system is
asymptotically stable. Discrete switching stabilizability is defined similarly
but requires the switching signal to be piecewise constant on intervals of
uniform length. In addition, we define feedback stabilizability in Filippov
sense (resp. sample-and-hold sense) as the existence of a feedback law under
which closed-loop Filippov solution (resp. sample-and-hold solution) is
asymptotically stable. It is proved that the four switching stabilizability
definitions are equivalent and their sufficient and necessary condition is the
existence of a piecewise quadratic control-Lyapunov function that can be
expressed as the pointwise minimum of a finite number of quadratic functions.
