H ∞ fault detection for 2-D T–S discrete stochastic fuzzy systems

Abstract

ABSTRACT This paper is concerned with fault detection (FD) problem for a class of two-dimensional (2-D) Takagi–Sugeno (T–S) discrete stochastic fuzzy systems. Based on the parallel distributed compensation (PDC), the fuzzy FD filter and the dynamics of FD system are constructed. Since the multiplicative property of the FD system would drastically increase the number of the stability conditions, a method of decoupling based on dimension expansion is used. By decoupling, the number of LMI-based stability conditions is reduced to r from by the conventional method. Then, the fuzzy FD filter is designed. The corresponding fuzzy FD system is proved to be mean-square asymptotically stable and satisfies the attenuation level for all disturbances. In addition, a theorem is proposed to prove that the stability conditions based on decoupling method are equivalent to those of conventional method. Finally, simulation examples are provided to demonstrate the usefulness of the proposed design methods.