Compensation-based state and fault estimation for IT2 polynomial fuzzy systems under both actuator and sensor faults

This paper presents a novel fault estimation method for interval type-2 (IT2) polynomial fuzzy systems (PFS) suffering from both sensor faults (SFs) and actuator faults (AFs) with unmeasurable premise variables (PVs). A compensation vector is proposed to compensate for the effects of the unmeasurable PVs, eliminating the restrictions of existing methods which require system stability or assume unmeasurable PVs to satisfy strict linear growth conditions. The designed observer eliminates singularity in AF estimation, while allowing unmatched membership functions (MFs) and different fuzzy rule numbers compared with the original system, thereby significantly enhancing the method's applicability and design flexibility. Furthermore, to reduce conservativeness, membership-function-dependent (MFD) conditions are introduced using information on the MFs, and an extended dissipative index is explored to establish a unified framework to address H_∞, passive, dissipative, and indices. In addition, a one-step solution approach is proposed to simplify the computational process for finding coupling parameters. Finally, comparative analyses with existing methods are presented, followed by simulations including a numerical example and a case study of a single-link rigid robot arm, to demonstrate effectiveness and advantages of the proposed method.