Limit cycles analysis of reset control systems with reset band

The reset band is a simple idea, and a must in practice, to improve reset compensation by adding extra phase lead in a feedback loop. However, a formal treatment of how the reset band can affect stability and performance of a reset control system is still an open issue. This work approaches the problem of the existence and stability of limit cycles of reset control systems with reset band. A frequency domain approach is given by using standard methods based on the describing function. In addition, closed-form expressions have been obtained for the describing function of arbitrary order full reset compensators with and without reset band.