A Unified Invariant-Set-Based Reliable Control Framework for T-S Fuzzy Systems with Actuator Saturation and Faults

This paper proposes a unified invariant-set-based reliable control framework for Takagi–Sugeno (T–S) fuzzy systems subject to actuator saturation and faults. The considered model incorporates both matched actuator faults and mismatched external disturbances, which provides a more realistic control setting. To address these challenges, a unified control framework is developed to systematically account for input constraints and actuator fault effects. A sequence of nested invariant ellipsoidal sets, together with corresponding set-dependent control gains, are constructed to guarantee that state trajectories starting within the designed outer invariant sets progressively converge toward a minimized target set. Based on this structure, relaxed LMI-based conditions are derived to compute both the invariant sets and the associated control laws via convex optimization. Finally, numerical examples demonstrate the effectiveness of the proposed method.