H∞ attenuation of disturbance switching over multiple frequency ranges

SummaryThis paper addresses the problem of switching control for systems subject to external disturbances that vary over multiple frequency ranges. Specifically, two different scenarios of disturbance injection are considered; namely, the disturbance may switch between different prescribed frequency ranges, subject to an average dwell time setting, or the disturbance may reside within one of the frequency ranges. To address these scenarios, a disturbance‐triggered control scheme is developed that divides the entire frequency range into low‐, mid‐, and high‐frequency ranges. This scheme ensures closed‐loop stability under average dwell time frequency‐range switching and achieves performance when operated under individual frequency ranges. Synthesis conditions in matrix inequalities are derived to characterize the switching control, and an iterative algorithm is proposed for finding a desired set of controller gains. Finally, two examples are presented to illustrate the effectiveness of the proposed control method.