A procedure for reachability analysis of rectangular automata

We present a procedure for the reachability analysis of rectangular automata. These automata form a subclass of hybrid automata, with the main restriction being that all derivatives, guards, and invariants are defined by constant lower and upper bounds in each dimension. Our procedure exploits these restrictions to provide more efficient and robust computations. Unlike a procedure that we described in earlier work, the procedure presented here is exact in any dimension, up to the representation of rationals. If limited precision is available for storing rationals, the procedure can be easily modified to yield very close over-approximations. We use a two-tank example to demonstrate the effectiveness of our approach.