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<p>A theory for error detection in linear digital state variable systems is described. With the aid of a tool called the gain matrix, it is shown that the effect of error propagation along different paths of the circuit can be analyzed. For circuits with operator fanout, it is shown that despite the fact that single faulty operators cause multiple state variables to be erroneous, no more additional check variables are required than for circuits without operator fanout. It is further shown that hardware optimization can be performed by sharing hardware functions between the original state variable system and its error detection circuitry. The analysis is performed for both single and multiple faulty operators. A scheme for error correction that performs error correction in real time is proposed. Experimental results that illustrate the practical viability of the proposed scheme are discussed.</p>
fault-tolerant linear digital state variable systems; error detection; gain matrix; error propagation; single faulty operators; hardware optimization; hardware functions; error correction; error correction; error detection; fault tolerant computing.

A. Chatterjee and M. d'Abreu, "The Design of Fault-Tolerant Linear Digital State Variable Systems: Theory and Techniques," in IEEE Transactions on Computers, vol. 42, no. , pp. 794-808, 1993.
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