Structural Analysis on Interval Matrices by Signed Digraph: Structural Perturbation Principle

This note deals with linear interval systems whose parameters in system matrix are expressed by intervals. We formalize the system reasoning about structures of interval systems by the structural perturbation principle: the interval system would have the interval property when its underlying sign structure include the component that has the corresponding sign property and the norm of the rest of component (considered structural 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.