Fault detection of discrete-time T–S fuzzy affine systems based on piecewise Lyapunov functions

This paper investigates the problem of robust fault detection for a class of discrete-time nonlinear systems, which are represented by Takagi–Sugeno (T–S) fuzzy affine dynamic models with norm-bounded uncertainties. The objective is to design an admissible fault detection filter guaranteeing the asymptotic stability of the resulting residual system with prescribed performances. It is assumed that the plant premise variables, which are often the state variables or their functions, are not measurable so that the fault detection filter implementation with state-space partition may not be synchronized with the state trajectories of the plant. Based on a piecewise quadratic Lyapunov function combined with S-procedure and some matrix inequality convexification techniques, the results are formulated in the form of linear matrix inequalities. Finally, a simulation example is provided to illustrate the effectiveness of the proposed approach.