Root clustering of a real matrix in a sector
SHAUL GUTMAN, F. Vaisberg · IEEE Transactions on Automatic Control · 1984
We prove that a real matrixA \in R^{n \times n}has all its eigenvalues in the left sector if and only if the polynomial det [\lambda^{2}I - 2\deltaA\lambda + (\delta^{2} + 1)A^{2}] is Hurwitz where δ is the sector's slope.