Observer-based Fault Detection for Piecewise Linear Systems: Discrete-time Cases

In this paper, we discuss the fault detection with unknown inputs for a class of discrete-time piecewise linear systems. Piecewise linear systems are mostly partitioned based on their state variables. Due to the system noise and estimation errors, the transitions of actual state and its estimate may not be synchronized, as well as the system modes. Motivated by the recent works [31], [29], [32], [30], [27], we consider the fault detection problem using non-synchronized observer and presents several less conservative design approaches.