A necessary and sufficient condition for the stability of interval matrices

Abstract

Consider the linear dynamical system described by the equation [xdot](t) = Ax(t) where A is a constant, real matrix with dimensions n × n, and the elements of matrix A are not known precisely. We know only the upper and lower bounds of the intervals in which the elements of matrix A are confined. In this paper, there is proved a necessary and sufficient condition for the stability of solutions of eqn. (1) with incomplete information about the elements of matrix A