Trajectory tracking in linear hybrid systems: an internal model principle approach

This paper deals with the problem of asymptotically tracking periodic trajectories for a class of hybrid systems (switched systems) having linear dynamics in each operating mode, where the reference trajectory and the control action are such that only isolated swithcing events occur. The possible presence of uncertainties in the system description is considered and no assumptions on the uniformity of dimension of the state vectors among modes are made. In order to deal with the hybrid nature of the considered system and the possible presence of discontinuities of its solutions at switching times, a properly amended tracking control problem is defined and a control strategy based on a discontinuous version of the classical internal model principle is proposed.