Reset control systems: The zero-crossing resetting law

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