High-Gain Observer-Based Fault-Tolerant Stabilisation for High-Order Sub-Fully Actuated Systems

In this note, an observer-based fault-tolerant stabilisation scheme is proposed for a class of high-order sub-fully actuated systems (sub-FASs) subject to both external disturbances and actuator faults. The FAS and sub-FAS approaches have emerged as effective solutions for nonlinear control and have been widely studied in recent years. However, output-feedback stabilisation for sub-FASs remains an open problem. To address this, a high-gain observer is first introduced to estimate the unmeasurable states of the system. Based on the observer's output, a robust adaptive control law is then developed to achieve local stabilisation. Using Lyapunov stability theory, the uniformly ultimately boundedness of the closed-loop solutions is rigorously proven. The effectiveness of the proposed method is validated through numerical simulations.