  A novel representation of reset control systems with a zero-crossing
resetting law, in the framework of hybrid inclusions, is postulated. The
problems of well-posedness and stability of the resulting hybrid dynamical
system are investigated, with a strong motivation in how non-deterministic
behavior is accomplished in control practice. Several stability conditions,
based on the eigenstructure of matrices related with periods of the reset
interval sequences, and on Lyapunov function-based conditions, are developed.
