Outer bounds on the real eingenvalues of interval matrices

Stability analysis of linear circuits and systems under interval parameter uncertainties can be equated to estimating the eigenvalues of interval matrices. In this paper, the problem of determining outer bounds on the ranges of the real eigenvalues is considered. A method for computing such bounds is suggested. It consist of setting up and solving a system of n nonlinear equations, n being the size of the original square interval matrix. The latter system is only mildly nonlinear and its solution poses no numerical difficulties. An example illustrating the applicability of the method suggested is provided. The approach adopted in bounding the real eigenvalues is rather general and can be extended to encompass the case of complex eigenvalues as well as to problems where the matrix elements are nonlinear functions of given interval parameters. Index Terms Robust stability analysis, eigenvalues of interval matrices.