Robust tracking and disturbance rejection in linear hybrid systems

Abstract

Robust tracking and disturbance rejection problem, which is commonly referred as the robust servomechanism problem, is considered for linear hybrid systems. The necessary and sufficient conditions for the existence of a solution to this problem are presented. It is shown that, these conditions are exact counterparts of the conditions in the case of linear continuous-state systems or linear discrete-event systems. Furthermore, as in the case of continuous-state systems or discrete-event systems, the solution (if exists) involves two parts: (i) a servocompensator which mimics the dynamics of the reference and disturbance; and (ii) a stabilizing compensator which asymptotically stabilizes the system obtained by augmenting the plant and the servocompensator.