A New Method of Fault Estimation Observer Design for T-S Fuzzy Singular Systems With Disturbances Using Dissipativity Theory

Abstract

This brief dedicates to addressing the robust fault estimation (FE) problem for a class of T-S fuzzy singular systems (TSFSSs) subject to faults and disturbances. A dissipativity-based FE observer design scheme is proposed to realize fault reconstruction, by which the FE performance can be improved in contrast to the existing one. With the help of the Lyapunov approach, dissipativity theory and matrix transformation technique, a brand-new condition is established to ensure observation error dynamics to be strictly <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(\mathscr {Q}, \mathscr {U}, \mathscr {R})-\iota -$ </tex-math></inline-formula> dissipative. It is worth mentioning that different from some previous studies, our method can solve observer gains simultaneously in a strict linear matrix inequality (LMI) framework rather than determine some of them artificially. Moreover, to bring extra degrees of freedom, slack scalars and matrices are added in FE observer design. The superiority of our method is fully illustrated via simulations.