Observer-based robust control for a class of sampled-data systems with model uncertainty and external disturbance

This paper studies the issue of observer-based feedback stabilisation for a class of linear sampled-data systems with model uncertainty and external disturbance. First, for a sampled-data system with external disturbance, a sampled-data observer is designed to estimate the system state. Subsequently, a robust H∞ controller based on the observer is developed. For a continuous sampling interval, the gain matrices of both observer and controller change exponentially. Second, using the state coordinate transformations with an exponential rate, a unified dynamics is constructed by augmenting the state estimation error and the closed-loop system state as a new state. Next, the sufficient conditions ensuring the asymptotical stability of the closed-loop system are given by the Lyapunov–Krasovskii method and linear matrix inequality (LMI) technique. Finally, the effectiveness of the proposed method is verified by a helicopter model.