Fault identification and reconfigurable control for bimodal piecewise affine systems

This paper addresses the design of a fault detection and reconfigurable control structure for bimodal piecewise affine (PWA) systems. The PWA bimodal system will be designed to verify input-to-state stability (ISS) in closed loop. The proposed methodology is divided into two parts. First, a Luenberger-based observer structure is proposed to solve the fault detection and identification (FDI) problem for bimodal PWA systems. The unknown value of the fault parameter is estimated by an observer equation, which is derived using a Lyapunov-based methodology. Then, the ISS property is proved for the observer. Second, a fault-tolerant state feedback controller is synthesized for the PWA model. The controller is designed to deal with partial loss of control authority identified by the observer. The ISS property is also proved for the controller. Finally, the ISS property for the interconnection of the controller and the observer-based fault identification mechanism is studied. The design procedure is formulated as a set of linear matrix inequalities (LMIs), which can be solved efficiently using available software packages.