2.47801m,,s -1.4471; 0.0518 I m22I -0.0194; 2 . 0 0 0 1 m~~~3 . 4 3 7 0 ; mq2= -0.7115; -0.0026s m 3 3 I -0.0012.We first show that this hyper-rectangle is strictly Hurwitz, i.e., that every matrix M E W is strictly Hurwitz. Since M is block diagonal, we can write where polynomials and matrices arising in robustness problems," in Proc. Conf. Inform. Sci. Sys., The Johns Hopkins Univ., Baltimore, MD, Root locations of an entire polytope of polynomials: It suffices to check the edges," in Proc. Amer. Contr. Conf., Minneapolis, MN, 1987. L. X. Xin, "Necessary and sufficient conditions for stability of a class of interval matrices," Int. J. Cont., vol. 45, no. I , pp. 211-214, 1987. [IO] B. R. Barmish and C . L. DeMarco, "A new method for improvement of robustness bounds for linear state equations," in Proc. Conf. Inform. Sci. Syst., Princeton Univ, Princeton, NJ, 1986. S . Bialas, "A necessary and sufficient condition for stability of interval matrices," Int. J. Conir., vol. 37, no. 4, pp. 717-722, 1983. B. R. Barmish and C. V. Hollot, "Counterexample to a recent result on the stability of interval matrices by S. Bialas," Ini. J. Cont., vol. 39, no. 5. pp. 1103-1 104, 1984. "A necessary and sufficient condition for the stability of convex combinations of stable polynomials or matrices," Bull. Polish Acad.Abstract-Polytopes of (characteristic) polynomials arise when systems experience real parameter variations. This paper presents a necessary and sufficient condition (requiring only a finite number of computations) for
