  We demonstrate the use of a new, control-oriented notion of finite state
approximation for a particular class of hybrid systems. Specifically, we
consider the problem of designing a stabilizing binary output feedback
switching controller for a pair of unstable homogeneous second order systems.
The constructive approach presented in this note, in addition to yielding an
explicit construction of a deterministic finite state approximate model of the
hybrid plant, allows us to efficiently establish a useable upper bound on the
quality of approximation, and leads to a discrete optimization problem whose
solution immediately provides a certifiably correct-by-design controller for
the original system. The resulting controller consists of a finite state
observer for the plant and a corresponding full state feedback switching
control law.
