Sufficient and necessary condition for the asymptotic stability of discrete linear interval systems

Abstract

In this paper, a sufficient and necessary condition for the asymptotic stability of the discrete linear interval system X(k + 1) = A1X(k) is presented; i.e. all the eigenvalues of each matrix AϵA1, (an interval matrix) have magnitudes less than 1 if and only if all the eigenvalues of every ‘extreme matrix’ of the interval matrix A1, have magnitudes less than 1.