Inequalities for the ’ h c e of Matrix Product

It is proved in this note that all Hurwitz polynomials of ordernot less than n form two simply connected Bore1 cones in the polynomialparameter space. Based on this result, edge theoremsfor Hurwitz sta-bility of general polyhedrons of polynomials and boundary theorems forHurwitz stability of compact sets of polynomials are obtained. Both casesof families of polynomials with dependent and independent coefficientsare considered. Different from the previous ones, our edge theoremsand boundary theorems are applicable to both monk and nonmonicpolynomical families and do not require the convexity or the connectivityof the set of polynomials. Moreover, our boundary theorem for families ofpolynomials with dependent coefficients does not require the coefficientdependency relation to be affine. Manuscript received July 21, 1993; revised December 20, 1993.G.-R. Duan is with the Department of Control Engineering, Harbin Institute M.-Z. Wang is with the Department of Mathematics, Harbin Institute of IEEE Log Number 9405667.of Technology, Harbin 150001, P.R. China. Technology, Harbin 150001, P.R. China. 0018-9286/94$04.00