Barmish, B. Ross; Fu, M.; Saleh, S. Stability of a polytope of matrices: Counterexamples. (English) Zbl 0644.93053 IEEE Trans. Autom. Control 33, No. 6, 569-572 (1988). The problem of robust stability leads to a considerable body of research on the stability of a polytope of polynomials, and matrices. Since Kharitonov’s seminal result on interval polynomials, there have been significant breakthroughts for the stability of a polytype of polynomials. However, for a polytope of matrices, the stability problem is far from completely resolved. In this paper, we provide counterexamples for three conjectures which are directly motivated by the results in the polynomial case. These counterexamples illustrate the fundamental differences between the polynomial stability problem and the matrix stability problem. Cited in 1 ReviewCited in 17 Documents MSC: 93D99 Stability of control systems 15A18 Eigenvalues, singular values, and eigenvectors 65G30 Interval and finite arithmetic Keywords:robust stability; polytype of polynomials; counterexamples; polynomial stability; matrix stability PDFBibTeX XMLCite \textit{B. R. Barmish} et al., IEEE Trans. Autom. Control 33, No. 6, 569--572 (1988; Zbl 0644.93053) Full Text: DOI Link