A fuzzy observer synthesis to state and fault estimation for Takagi-Sugeno implicit systems

The present paper inquire a fuzzy observer design issue for continuous time Takagi-Sugeno aiming at estimating both of fault and state in case of unmeasurable premise variables. Thanks to singular value decomposition (SVD) approach, the fuzzy observer is synthesized in explicit form. The developed method is based on augmented structure that assemble state and actuator fault, sensor fault as well as their sequential derivatives is enjoined to institute the destined observer. The Lyapunov function is analyzed to assume the exponential stability of the studied observer, furthermore convergence conditions are expressed as linear matrix inequalities (LMIs) form. The applicability of the nominated theoritical result is elucidated and confiremed through numerical simulation using an example of an implicit fuzzy model.