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Stability of a polytope of matrices: Counterexamples. (English) Zbl 0644.93053
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.

93D99Stability of control systems
15A18Eigenvalues, singular values, and eigenvectors
65G30Interval and finite arithmetic
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