Some tests to determine the Hurwitz-stability and the Schur-stability of an interval matrix

In this paper we describe a sufficient condition by means of a simpler test that guarantees stability of a linear time-invariant system with parametric uncertainty in the “A” matrix, The parametric uncertainty is represented by an interval matrix. The proposed test is simpler than the existing ones. It is based on the eigenvalues of the Hermitian part of L and P (for the continuous case), and the spectral radius of the Hermitian and skew-Hermitian part of L and P. An upper bound for the continuous case φ is derived from their maximum eigenvalues; and and upper bound for the discrete case ξ, is derived from their spectral radius. The results presented are for the general case of an interval matrix