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Schur stability of convex combination of matrices. (English) Zbl 0703.15014
Necessary and sufficient conditions are derived for Schur stability (maintenance of the matrix property that all eigenvalues have magnitude less than one) of all convex combinations of two (n,n) matrices. The stability regions considered are circles.
Reviewer: G.Sierksma

15A42Inequalities involving eigenvalues and eigenvectors
52A20Convex sets in $n$ dimensions (including convex hypersurfaces)
Full Text: DOI
[1] Bialas, S.: A necessary and sufficient condition for the stability of convex combinations of stable polynomials and matrices. Bull. Polish acad. Sci. tech. Sci. 33, No. 9--10, 473-480 (1985) · Zbl 0607.93044
[2] Fu, M.; Barmish, B. R.: Stability of convex and linear combinations of polynomials and matrices arising in robustness problems. Proceedings of the 1987 conference on information science and systems (1987)
[3] Lancaster, P.; Tismenetsky, M.: The theory of matrices. (1985) · Zbl 0558.15001
[4] Ortega, J. M.: Matrix theory. (1987) · Zbl 0654.15001