  This paper introduces a closed-loop frequency analysis tool for reset control
systems. To begin with sufficient conditions for the existence of the
steady-state response for a closed-loop system with a reset element and driven
by periodic references are provided. It is then shown that, under specific
conditions, such a steady-state response for periodic inputs is periodic with
the same period as the input. Furthermore, a framework to obtain the
steady-state response and to define a notion of closed-loop frequency response,
including high order harmonics, is presented. Finally, pseudo-sensitivities for
reset control systems are defined. These simplify the analysis of this class of
systems and allow a direct software implementation of the analysis tool. To
show the effectiveness of the proposed analysis method the position control
problem for a precision positioning stage is studied. In particular, comparison
with the results achieved using methods based on the Describing Function shows
that the proposed method achieves superior closed-loop performance.
