  The minimum-time control problem consists in finding a control policy that
will drive a given dynamic system from a given initial state to a given target
state (or a set of states) as quickly as possible. This is a well-known
challenging problem in optimal control theory for which closed-form solutions
exist only for a few systems of small dimensions. This paper presents a very
generic solution to the minimum-time problem for arbitrary discrete-time linear
systems. It is a numerical solution based on sparse optimization, that is the
minimization of the number of nonzero elements in the state sequence over a
fixed control horizon. We consider both single input and multiple inputs
systems. An important observation is that, contrary to the continuous-time
case, the minimum-time control for discrete-time systems is not necessarily
entirely bang-bang.
