Joint State, Disturbance and Fault Estimation for Weakly Output Redundant Discrete-Time Linear Systems

The problem considered in this paper is dual to the control problem for over-actuated systems found in the literature. We show that, due to a certain notion of weak output redundancy, there always exists an unobservability subspace containing the input subspace, which ensures that the original system can be partitioned into two subsystems, one of which is not affected by actuator faults. We use this fact to estimate the disturbance and the fault in a cascaded fashion: we first design a discrete-time filter on a properly designed residual signal, that can reconstruct the disturbance. The estimated disturbance can then be used to perform fault detection and estimation in a cascaded fashion. A numerical example verifies the efficacy of the proposed strategy.