Non-concurrent Error Detection and Correction in Switched Linear Controllers

In this paper, we consider protection schemes for linear timeinvariant (LTI) controllers in switched systems. These controllers are often digital in nature and, as such, are subject to internal hardware malfunctions (faults). A discrete-time (DT) LTI system is usually protected against faults by embedding the state-space of the original system into the state-space of a higher dimensional redundant system. These embeddings preserve the state evolution of the original system in some encoded form, but enable error detection and correction through concurrent parity checks (i.e., parity checks that are performed at the end of each time step). In this paper, we present a systematic method of constructing linear embeddings for protecting switched DT LTI controllers. These methodologies allow an external mechanism to detect and identify transient state-transition faults through non-concurrent (e.g., periodic) parity checks. The resulting error detection and correction procedures can then be performed periodically, thereby relaxing the requirements on the reliability of the checking mechanism.