Fault-tolerant Control of Discrete-time Descriptor Systems using Virtual Actuators

This paper proposes a fault-tolerant control (FTC) strategy based on virtual actuators for discrete-time descriptor systems subject to multiplicative and additive actuator faults. The goal of this FTC strategy is to reconfigure the closed-loop system by means of a virtual actuator that allows maintaining the use of the nominal controller without having to retune it. In order to achieve this goal, we define the structure of a dynamical virtual actuator for descriptor systems including multiplicative and additive actuator faults. In order to use a state-feedback controller for implementing the FTC strategy, a state observer for descriptor systems is also defined. Under the proposed FTC scheme, the separation principle of the virtual actuator, the nominal closed-loop system and the state observer is established. Therefore, all the gains can be designed separately. Finally, a numerical example is provided to show the effectiveness of the proposed FTC strategy.