## Structured Redundancy for Fault Tolerance in LTI State-Space Models and Petri Nets (1999)

Venue: | Kybernetika |

Citations: | 9 - 9 self |

### BibTeX

@ARTICLE{Hadjicostis99structuredredundancy,

author = {C. N. Hadjicostis and G. C. Verghese},

title = {Structured Redundancy for Fault Tolerance in LTI State-Space Models and Petri Nets},

journal = {Kybernetika},

year = {1999},

volume = {35},

pages = {39--55}

}

### OpenURL

### Abstract

The design and implementation of dynamic systems has traditionally focused on minimal representations which require the least number of state variables. However, \structured redundancy" | redundancy that has been intentionally introduced in some systematic way | can be extremely important when fault tolerance is desired. The redundancy can be used to detect and correct errors or to guarantee desirable performance despite hardware or computational failures. Modular redundancy, the traditional approach to fault tolerance, is prohibitively expensive because of the overhead in replicating the hardware. This paper discusses alternative methods for systematically introducing redundancy in dynamic systems. Our approach consists of mapping the state space of the original system into a redundant space of higher dimension while preserving the properties of the original system in some encoded form within this larger space. We illustrate our approach by focusing on linear time-invariant (LTI) dyna...

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Citation Context ... asynchronous, distributed, nondeterministic, and/or stochastic systems. They are particularly relevant to the study of discrete event systems (DES); theory, examples and applications can be found in =-=[1, 4, 18, 22]-=-. A Petri net is represented by a directed, bipartite graph with two kinds of nodes: places (denoted by fp 1 ; p 2 ; :::; p n g and drawn as circles) and transitions (denoted by ft 1 ; t 2 ; :::; t m ... |

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Citation Context ...verly tailored to the specic application under consideration. More broadly applicable and systematic approaches for introducing redundancy in computational systems were studied recently by Beckmann, [=-=2, 3]-=-, and later by us, [10, 11]. Beckmann's work focused on computations that can be modeled as abelian group operations, and used group homomorphisms both to introduce redundancy and to analyze its prope... |

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Citation Context ...ation, a single fault causes the value of a single state variable (in x[k] or [k]) to be incorrect. Such an error model is appropriate for Petri net models ofsnite state machines or linear automata, [=-=24, 25] (-=-because single-bit errors corrupt a single place of the Petri net). Other error models are also possible. If we apply the similarity transformation [k] = T [k], where T is given by " I n 0 C I ... |

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Citation Context ...verly tailored to the specic application under consideration. More broadly applicable and systematic approaches for introducing redundancy in computational systems were studied recently by Beckmann, [=-=2, 3]-=-, and later by us, [10, 11]. Beckmann's work focused on computations that can be modeled as abelian group operations, and used group homomorphisms both to introduce redundancy and to analyze its prope... |

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