An approximate method for the standard interval eigenvalue problem of real non‐symmetric interval matrices

Abstract

AbstractIn this study, we discuss an approximate method for estimating the upper and lower bounds on the set of all possible eigenvalues of the standard interval eigenvalue problem of the real non‐symmetric interval matrix. This kind of eigenvalue problem involves non‐probabilistic uncertainties. The favourable bound estimate is actually a set in eigenvalue space rather than a single vector. The obtained estimate is the calculable set which contains the true eigenvalues of the interval uncertain systems. In this study, first of all, we give a review of Deif's solution theorem for the standard interval eigenvalue problem in real non‐symmetric interval matrices, then we present the interval perturbation method for estimating the set of all possible eigenvalues of the real non‐symmetric interval matrix. Very weak condition of solution and inexpensive computational effort are the characteristics of the present interval perturbation method. The comparison example shows that the interval eigenvalues produced by the interval perturbation method show good agreement with those obtained by Deif's solution theorem. A numerical example of the Automobile Suspension System illustrates the application of the proposed method. Copyright © 2001 John Wiley & Sons, Ltd.