Reliable control of discrete-time linear systems with actuator failure

A sufficient condition is given for robust stability of a discrete linear system in which an arbitrary portion of input channel is permanently attenuated or disconnected due to actuator fault. The partial disconnection/attenuation of the control input, is modelled as uncertainty and dealt with via a robust control method. The proposed method enables one to design a controller in such a way that the closed loop system remains stable when any combination of input signals is disconnected if the open loop system is stable and fulfils some additional properties. It is shown that the linear quadratic regulator can guarantee reliable closed loop with some specific choices for weighting matrices. The result is extended to unstable systems by assuming additional constraints on the failed actuators. Compared to previously established results, the proposed conditions are easier to verify and applicable to a wider class of systems. An example is also included.