Error-Separation-Based Robust Control for Linear Systems with Model Mismatch and External Disturbances

This paper proposes a fault-resilient robust control framework based on state error separation to ensure stable and robust operation of linear systems under model mismatch and unknown external disturbances. A test-then-control strategy is developed to online detect and classify the influence of model mismatch and disturbances, thereby enabling real-time reconfiguration of the feedback control gain. Specifically, within each test interval, a test control input is applied to both the nominal and real systems, generating their respective state trajectories. A least-squares-based separation algorithm is then employed to decouple the state errors induced by model mismatch and external disturbances. Based on the identified mismatch and disturbance indices, the controller adaptively updates the control law to maintain stability and fault resilience. Through this cyclic detection–control process, a safe closed-loop control sequence is achieved that guarantees the desired performance even under uncertain or degraded conditions. The accuracy of the detection indicators and the effectiveness of the proposed algorithm in maintaining stability, robustness, and safety are demonstrated through numerical simulations.