State-Space Analysis of Discrete-Time Disturbance Observer for Sampled-Data Control Systems

We present a state-space analysis of discrete-time disturbance observer (DOB) for a class of sampled-data control systems. Unlike the continuous-time case, it is well-known that sampling process may yield non-minimum phase zeros (called sampling zeros). Motivated by the truncated Taylor series (TTS) model which well describes the behavior of sampling zeros in the state-space, we present a condition for robust stability of the uncertain sampled-data control system with the discrete-time DOB. In particular, using the discrete-time singular perturbation theory, we show that the uncertain plant with disturbance behaves like a disturbance-free nominal model with the help of the discrete-time DOB.