A controllability result for piecewise-linear hybrid systems

A piecewise-linear hybrid system is a dynamic system which is the product of a finite-state automaton and a family of affine systems on polytopes. In full generality, determination of the controllability of such systems is undecidable. For control synthesis it is therefore of interest to determine subclasses of such systems for which the problem is decidable. In this paper an approach to controllability is described for which the problem decomposes into a reachability problem for a finite-state automaton and one for a family of affine systems on polytopes. For a subclass of such systems an equivalent condition for reachability of a piecewise-linear hybrid system is summarized. The solution to the subproblem of control to a facet of a polytope is presented.