Redundant Implementations of Discrete-Time Linear Time-Invariant Dynamic Systems

This chapter discusses fault tolerance in discrete-time linear time-invariant (LTI) dynamic systems [Hadjicostis and Verghese, 1997; Hadjicostis and Verghese, 1999; Hadjicostis, 1999]. It focuses on redundant implementations that reflect the state of the original system into a larger LTI dynamic system in a linearly encoded form. In essence, this chapter restricts attention to discrete-time LTI dynamic systems and linear coding techniques, both of which are rather standard and well-developed topics in system and coding theory respectively. Interestingly enough, the combination of linear dynamics and coding reveals some novel aspects of the problem, as summarized by the characterization of the class of appropriate redundant implementations given in Theorem 5.1. In most of the fault-tolerance schemes discussed, error detection and correction is performed at the end of each time step, although examples of non-concurrent schemes are also presented [Hadjicostis, 2000; Hadjicostis, 2001].