Non-Concurrent Error Detection and Correction in Fault-Tolerant Discrete-Time LTI Dynamic Systems

This paper develops resource-efficient alternatives to modular redundancy for fault-tolerant discrete-time (DT) linear time-invariant (LTI) dynamic systems. The proposed method extends previous approaches that are based on embedding the state of a given DT LTI dynamic system into the redundant state-space of a DT LTI dynamic system of higher state dimension. These embeddings, as well as the embeddings studied in this paper, preserve the state evolution of the original system in some linearly encoded form and allow error detection and correction to be performed through concurrent parity checks (i.e., parity checks that are evaluated at the end of each time step). The novelty of the approach developed in this paper relies on carefully choosing the redundant dynamics of the fault-tolerant implementation in a way that allows parity checks to capture the evolution of errors in the system and, based on nonconcurrent parity checks (e.g., parity checks that are evaluated periodically), uniquely determine the initial value of each error, the time step at which it took place and the state variable it originally affected. The resulting error detection, identification, and correction procedures can be performed periodically and can significantly reduce the overhead, complexity and reliability requirements on the checking mechanism.