Robust disturbance rejection for uncertain linear system with time-varying exo-system: A disturbance observer approach

This paper addresses the problem of completely eliminating modeled disturbance that enters linear minimum-phase systems having parametric uncertainty and is generated by a linear time-varying exo-system. Motivated by the internal model principle (IMP), the core is to append a filter in front of the plant, such that (a) the disturbance model is embedded into the filter dynamics and (b) the filter is of minimum phase. Then the cascade connection of the plant and the filter is robustly stabilized by employing a disturbance observer (DOB)-based controller. In addition to simplicity in the design over the existing IMP-based approaches, the proposed controller also enjoys benefits of the DOB techniques, such as robustness against large parametric uncertainty and additional unmodeled disturbance, and guaranteeing a pre-defined nominal tracking performance in both transient and steady-state. Stability and performance of the controller are analyzed by the singular perturbation theory.