  We consider here systems with piecewise linear dynamics that are periodically
sampled with a given period {\tau} . At each sampling time, the mode of the
system, i.e., the parameters of the linear dynamics, can be switched, according
to a switching rule. Such systems can be modelled as a special form of hybrid
automata, called "switched systems", that are automata with an infinite real
state space. The problem is to find a switching rule that guarantees the system
to still be in a given area V at the next sampling time, and so on
indefinitely. In this paper, we will consider two approaches: the indirect one
that abstracts the system under the form of a finite discrete event system, and
the direct one that works on the continuous state space.
  Our methods rely on previous works, but we specialize them to a simplified
context (linearity, periodic switching instants, absence of control input),
which is motivated by the features of a focused case study: a DC-DC boost
converter built by electronics laboratory SATIE (ENS Cachan). Our enhanced
methods allow us to treat successfully this real-life example.
