A generalized framework for robust stability analysis of discrete-time disturbance observer for sampled-data systems: A fast sampling approach

As a robust controller to compensate both model uncertainty and external disturbances, the disturbance observer (DOB) has been widely employed in a number of industrial applications, typically implemented in a discrete-time fashion for sampled-data systems. Substantial research effort has gone into the study on how to design the discrete-time DOB over the past decades, yet there is still no unified approach to robust stability analysis for the various types of DOBs. In this paper, by representing these variations into a general structure, we present a generalized framework for stability analysis that is available in whichever way the discrete-time DOB is designed and regardless of how large the model uncertainty is. As a consequence of the generalization, an almost necessary and sufficient stability condition under fast sampling is presented. Motivated by this new stability condition, a systematic design guideline for the discrete-time DOB is proposed in order to guarantee the robust stabilization against arbitrarily large (but bounded) model uncertainty. The validity of the presented analysis and design procedure is verified by an illustrative example.