Fault Detection and Isolation for a Class of Nonlinear Systems Based on Gerschgorin Theorem and Optimization Approach

This article is concerned with the fault detection and isolation (FDI) problem for a class of nonlinear systems described by the T–S fuzzy models. Based on the concept of minimum unobservability subspace and geometric property of factor space, a set of FDI filters where each residual is only affected by one fault and completely decoupled from other faults is designed. Furthermore, in the decoupling space, the
$H_{\infty }/H_{-}$
performance indexes are provided to enhance the sensitivity of residual to faults and robustness to disturbances. In particular, to solve the nonconvex filter design problem caused by introducing the
$H_{-}$
index, the Gerschgorin theorem is first used to linearize the corresponding filter design conditions in the outer region of a ball. Then, the FDI filter design problem is converted into a convex optimization one, which is solved via the linear matrix inequality (LMI) control Toolbox, and the advantages and effectiveness of the proposed FDI method are verified through two simulation examples.