Co-Design of Functional Interval Observer-Based Control for Uncertain Linear Parameter Varying Switched Systems

This paper presents a novel method for the co-design of observers and controllers for switched linear parameter-varying (LPV) systems subject to unknown but bounded uncertainties, disturbances, and faults. First, a polytopic functional interval observer (FIO) is employed to estimate the lower and upper bounds of the system states. Next, a proportional-integral (PI) observer is designed to estimate fault signals accurately. Building on these estimates, a fault-tolerant control (FTC) strategy is developed to ensure the stability of the closed-loop system and maintain reference model tracking in the presence of faults. The sufficient conditions for the existence of observers and controllers are derived using Linear Matrix Inequalities (LMIs), leveraging multiple Lyapunov functions and ensuring input-to-state stability (ISS) under the average dwell time (ADT) approach. Finally, the effectiveness of the proposed approach is validated through a simulation applied to vehicle lateral dynamics estimation and control.