Reasoning about Structure of Interval Systems: An Approach by Sign Directed-Graph

Yoshiteru Ishida and Atusi Nogi

This paper deals with qualitative and structural reasoning on linear interval systems whose parameters are specified by intervals. We formalize the systems of reasoning about structures of interval systems by the qualitative perturbation principle: the interval system would have the interval property when its underlying sign structure include the componenthat has the corresponding sign property and the norm of the rest of component (considered qualitative perturbation) is small enough. Several interval properties of interval matrix such as nonsingularity, rank and inverse stability will be discussed by applying the principle to the graphical conditions for the corresponding sign properties. The Klein model in economics is used as an illustrative example.


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