LMI-based approach to robust fault detection for uncertain discrete-time piecewise affine slab systems

This paper investigates the problem of fault detection for a class of uncertain discrete-time piecewise affine systems. 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 piecewise affine systems are partitioned based on the state space instead of the measurable output space so that the filter implementations may not be synchronized with the plant state trajectory transitions. Based on a piecewise quadratic Lyapunov function combined with S-procedure and some matrix inequality convexifying 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.