Stability of reset control systems with inputs

This work extends previous stability results of autonomous reset control systems to the case in which external inputs, such as references and disturbances inputs, are present. The H_beta-condition, that has been developed in the framework of Lyapunov stability for the autonomous system, has been used and extended to approach the problem of input-output stability. By using a passivity approach, L₂-stability of reset control systems is investigated. First, with respect to reference inputs and full reset compensation, by directly using the H_beta-condition; and secondly, with respect to both reference and disturbance inputs, and allowing partial or full reset, where a new condition referred to as the H_gamma-condition is developed.