Fault Detection and Isolation for a Class of Nonlinear Systems Based on Gerschgorin Theorem and Optimization Approach
针对T-S模糊模型描述的非线性系统，设计一组故障检测与隔离滤波器，使每个残差只受一个故障影响，并利用Gerschgorin定理将非凸滤波器设计转化为凸优化问题，通过LMI工具箱求解。
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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }/H_{-}$ </tex-math></inline-formula> 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{-}$ </tex-math></inline-formula> 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.